exponential functions - university of nebraska–lincolntlai3/m119-section15.pdf · 2016-11-09 ·...
TRANSCRIPT
![Page 1: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/1.jpg)
Exponential Functions
September 4, 2013
Exponential Functions
![Page 2: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/2.jpg)
Population Growth
Year 2000 2001 2002 2003 2004 2005 2006Population 2.020 2.093 2.168 2.246 2.327 2.411 2.498
Table: The population (in millions) of Nevada 2000–2006.
Review questions:
Is this population function increasing?
Is this population a linear function?
Is this population a concave up or concave down function? Why?
Find the relative change for each year between 2000 and 2003.
Exponential Functions
![Page 3: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/3.jpg)
Population Growth
Year 2000 2001 2002 2003 2004 2005 2006Population 2.020 2.093 2.168 2.246 2.327 2.411 2.498
Table: The population (in millions) of Nevada 2000–2006.
Review questions:
Is this population function increasing?
Is this population a linear function?
Is this population a concave up or concave down function? Why?
Find the relative change for each year between 2000 and 2003.
Exponential Functions
![Page 4: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/4.jpg)
Population Growth
Year 2000 2001 2002 2003 2004 2005 2006Population 2.020 2.093 2.168 2.246 2.327 2.411 2.498
Table: The population (in millions) of Nevada 2000–2006.
Review questions:
Is this population function increasing?
Is this population a linear function?
Is this population a concave up or concave down function? Why?
Find the relative change for each year between 2000 and 2003.
Exponential Functions
![Page 5: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/5.jpg)
Population Growth
Year 2000 2001 2002 2003 2004 2005 2006Population 2.020 2.093 2.168 2.246 2.327 2.411 2.498
Table: The population (in millions) of Nevada 2000–2006.
Review questions:
Is this population function increasing?
Is this population a linear function?
Is this population a concave up or concave down function? Why?
Find the relative change for each year between 2000 and 2003.
Exponential Functions
![Page 6: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/6.jpg)
Population Growth
Year 2000 2001 2002 2003 2004 2005 2006Population 2.020 2.093 2.168 2.246 2.327 2.411 2.498
Table: The population (in millions) of Nevada 2000–2006.
Population grew by about 3.6% between 2000–2001, 2001–2002,2002–2003
Rule: Whenever we have constant percent increase, we have anexponential growth.
Let t be the number of years since 2000, then the population isgiven by
P = 2.020(1.036)t .
The population is an exponential function (with respect to t).
1.036 represents the factor by which the population grows eachyear. It is called the growth factor.
Exponential Functions
![Page 7: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/7.jpg)
Population Growth
Year 2000 2001 2002 2003 2004 2005 2006Population 2.020 2.093 2.168 2.246 2.327 2.411 2.498
Table: The population (in millions) of Nevada 2000–2006.
Population grew by about 3.6% between 2000–2001, 2001–2002,2002–2003
Rule: Whenever we have constant percent increase, we have anexponential growth.
Let t be the number of years since 2000, then the population isgiven by
P = 2.020(1.036)t .
The population is an exponential function (with respect to t).
1.036 represents the factor by which the population grows eachyear. It is called the growth factor.
Exponential Functions
![Page 8: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/8.jpg)
Population Growth
Year 2000 2001 2002 2003 2004 2005 2006Population 2.020 2.093 2.168 2.246 2.327 2.411 2.498
Table: The population (in millions) of Nevada 2000–2006.
Population grew by about 3.6% between 2000–2001, 2001–2002,2002–2003
Rule: Whenever we have constant percent increase, we have anexponential growth.
Let t be the number of years since 2000, then the population isgiven by
P = 2.020(1.036)t .
The population is an exponential function (with respect to t).
1.036 represents the factor by which the population grows eachyear. It is called the growth factor.
Exponential Functions
![Page 9: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/9.jpg)
Population Growth
Year 2000 2001 2002 2003 2004 2005 2006Population 2.020 2.093 2.168 2.246 2.327 2.411 2.498
Table: The population (in millions) of Nevada 2000–2006.
Population grew by about 3.6% between 2000–2001, 2001–2002,2002–2003
Rule: Whenever we have constant percent increase, we have anexponential growth.
Let t be the number of years since 2000, then the population isgiven by
P = 2.020(1.036)t .
The population is an exponential function (with respect to t).
1.036 represents the factor by which the population grows eachyear. It is called the growth factor.
Exponential Functions
![Page 10: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/10.jpg)
Population Growth
Year 2000 2001 2002 2003 2004 2005 2006Population 2.020 2.093 2.168 2.246 2.327 2.411 2.498
Table: The population (in millions) of Nevada 2000–2006.
Population grew by about 3.6% between 2000–2001, 2001–2002,2002–2003
Rule: Whenever we have constant percent increase, we have anexponential growth.
Let t be the number of years since 2000, then the population isgiven by
P = 2.020(1.036)t .
The population is an exponential function (with respect to t).
1.036 represents the factor by which the population grows eachyear. It is called the growth factor.
Exponential Functions
![Page 11: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/11.jpg)
Population Growth
Assuming that the formula holds for 50 years (since 2000).
Exponential Functions
![Page 12: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/12.jpg)
Elimination of Drug from the Body
Problem 1. When a patient is given medication, the drug entersthe bloodstream. The rate at which the drug is metabolized andeliminated depends on the particular drug. For the antibioticampicillin, approximately 40% of the drug eliminated every hour. Atypical dose of ampicillin is 250 mg. Suppose Q = f (t), where Qis the quantity of ampicillin, in mg, in the bloodstream at time thours since the drug was given. Find several initial values of f (t).
f (0) = 250
f (1) = 250(0.6) = 150
f (2) = 250(0.6)(0.6) = 250(0.6)2 = 90
f (3) = 250(0.6)2(0.6) = 250(0.6)3 = 54
f (4) = 32.4
f (5) = 19.4
Exponential Functions
![Page 13: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/13.jpg)
Elimination of Drug from the Body
Problem 1. When a patient is given medication, the drug entersthe bloodstream. The rate at which the drug is metabolized andeliminated depends on the particular drug. For the antibioticampicillin, approximately 40% of the drug eliminated every hour. Atypical dose of ampicillin is 250 mg. Suppose Q = f (t), where Qis the quantity of ampicillin, in mg, in the bloodstream at time thours since the drug was given. Find several initial values of f (t).
f (0) = 250
f (1) = 250(0.6) = 150
f (2) = 250(0.6)(0.6) = 250(0.6)2 = 90
f (3) = 250(0.6)2(0.6) = 250(0.6)3 = 54
f (4) = 32.4
f (5) = 19.4
Exponential Functions
![Page 14: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/14.jpg)
Elimination of Drug from the Body
Problem 1. When a patient is given medication, the drug entersthe bloodstream. The rate at which the drug is metabolized andeliminated depends on the particular drug. For the antibioticampicillin, approximately 40% of the drug eliminated every hour. Atypical dose of ampicillin is 250 mg. Suppose Q = f (t), where Qis the quantity of ampicillin, in mg, in the bloodstream at time thours since the drug was given. Find several initial values of f (t).
f (0) = 250
f (1) = 250(0.6) = 150
f (2) = 250(0.6)(0.6) = 250(0.6)2 = 90
f (3) = 250(0.6)2(0.6) = 250(0.6)3 = 54
f (4) = 32.4
f (5) = 19.4
Exponential Functions
![Page 15: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/15.jpg)
Elimination of Drug from the Body
Problem 1. When a patient is given medication, the drug entersthe bloodstream. The rate at which the drug is metabolized andeliminated depends on the particular drug. For the antibioticampicillin, approximately 40% of the drug eliminated every hour. Atypical dose of ampicillin is 250 mg. Suppose Q = f (t), where Qis the quantity of ampicillin, in mg, in the bloodstream at time thours since the drug was given. Find several initial values of f (t).
f (0) = 250
f (1) = 250(0.6) = 150
f (2) = 250(0.6)(0.6) = 250(0.6)2 = 90
f (3) = 250(0.6)2(0.6) = 250(0.6)3 = 54
f (4) = 32.4
f (5) = 19.4
Exponential Functions
![Page 16: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/16.jpg)
Elimination of Drug from the Body
Problem 1. When a patient is given medication, the drug entersthe bloodstream. The rate at which the drug is metabolized andeliminated depends on the particular drug. For the antibioticampicillin, approximately 40% of the drug eliminated every hour. Atypical dose of ampicillin is 250 mg. Suppose Q = f (t), where Qis the quantity of ampicillin, in mg, in the bloodstream at time thours since the drug was given. Find several initial values of f (t).
f (0) = 250
f (1) = 250(0.6) = 150
f (2) = 250(0.6)(0.6) = 250(0.6)2 = 90
f (3) = 250(0.6)2(0.6) = 250(0.6)3 = 54
f (4) = 32.4
f (5) = 19.4
Exponential Functions
![Page 17: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/17.jpg)
Elimination of Drug from the Body
Problem 1. When a patient is given medication, the drug entersthe bloodstream. The rate at which the drug is metabolized andeliminated depends on the particular drug. For the antibioticampicillin, approximately 40% of the drug eliminated every hour. Atypical dose of ampicillin is 250 mg. Suppose Q = f (t), where Qis the quantity of ampicillin, in mg, in the bloodstream at time thours since the drug was given. Find several initial values of f (t).
f (0) = 250
f (1) = 250(0.6) = 150
f (2) = 250(0.6)(0.6) = 250(0.6)2 = 90
f (3) = 250(0.6)2(0.6) = 250(0.6)3 = 54
f (4) = 32.4
f (5) = 19.4
Exponential Functions
![Page 18: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/18.jpg)
Elimination of Drug from the Body
Is this linear? Increasing? Decreasing? Concave up? Concavedown?
Find the formula of Q = f (t).
Exponential Functions
![Page 19: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/19.jpg)
Elimination of Drug from the Body
Is this linear? Increasing? Decreasing? Concave up? Concavedown?
Find the formula of Q = f (t).
Exponential Functions
![Page 20: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/20.jpg)
Elimination of Drug from the Body
Q = f (t) = 250(0.6)t
This function is called an exponential decay function.
Exponential Functions
![Page 21: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/21.jpg)
Elimination of Drug from the Body
Q = f (t) = 250(0.6)t
This function is called an exponential decay function.
Exponential Functions
![Page 22: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/22.jpg)
Elimination of Drug from the Body
Q = f (t) = 250(0.6)t
This function is called an exponential decay function.
Exponential Functions
![Page 23: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/23.jpg)
The General Exponential Function
Definition
We say that P is an exponential function of t with base a if
P = P0at .
P0 is the initial quantity.
a is the factor by which P changes when t increase by 1.
If a > 1, we have an exponential growth.
If 0 < a < 1, we have an exponential decay.
a = 1 + r , where r is the decimal representation of thepercent rate of change.
Exponential Functions
![Page 24: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/24.jpg)
The General Exponential Function
Definition
We say that P is an exponential function of t with base a if
P = P0at .
P0 is the initial quantity.
a is the factor by which P changes when t increase by 1.
If a > 1, we have an exponential growth.
If 0 < a < 1, we have an exponential decay.
a = 1 + r , where r is the decimal representation of thepercent rate of change.
Exponential Functions
![Page 25: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/25.jpg)
The General Exponential Function
Definition
We say that P is an exponential function of t with base a if
P = P0at .
P0 is the initial quantity.
a is the factor by which P changes when t increase by 1.
If a > 1, we have an exponential growth.
If 0 < a < 1, we have an exponential decay.
a = 1 + r , where r is the decimal representation of thepercent rate of change.
Exponential Functions
![Page 26: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/26.jpg)
The General Exponential Function
Definition
We say that P is an exponential function of t with base a if
P = P0at .
P0 is the initial quantity.
a is the factor by which P changes when t increase by 1.
If a > 1, we have an exponential growth.
If 0 < a < 1, we have an exponential decay.
a = 1 + r , where r is the decimal representation of thepercent rate of change.
Exponential Functions
![Page 27: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/27.jpg)
The General Exponential Function
Definition
We say that P is an exponential function of t with base a if
P = P0at .
P0 is the initial quantity.
a is the factor by which P changes when t increase by 1.
If a > 1, we have an exponential growth.
If 0 < a < 1, we have an exponential decay.
a = 1 + r , where r is the decimal representation of thepercent rate of change.
Exponential Functions
![Page 28: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/28.jpg)
Comparison between Linear and Exponential Functions
Definition
A linear function has a constant rate of change.
An exponential function has a constant percent rate of change(relative rate of change).
Exponential Functions
![Page 29: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/29.jpg)
Comparison between Linear and Exponential Functions
Definition
A linear function has a constant rate of change.
An exponential function has a constant percent rate of change(relative rate of change).
Exponential Functions
![Page 30: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/30.jpg)
Example
Problem 2. A quantity can change rapidly. Suppose the initialvalue is 100. Find the formula for the quantity Q at the time tminutes later if Q is:
Increasing by 3 per minute.
Decreasing by 7 per minute.
Increasing by 4% per minute.
Decreasing by 6% per minute.
Exponential Functions
![Page 31: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/31.jpg)
Example
Problem 2. A quantity can change rapidly. Suppose the initialvalue is 100. Find the formula for the quantity Q at the time tminutes later if Q is:
Increasing by 3 per minute.
Decreasing by 7 per minute.
Increasing by 4% per minute.
Decreasing by 6% per minute.
Exponential Functions
![Page 32: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/32.jpg)
Example
Problem 2. A quantity can change rapidly. Suppose the initialvalue is 100. Find the formula for the quantity Q at the time tminutes later if Q is:
Increasing by 3 per minute.
Decreasing by 7 per minute.
Increasing by 4% per minute.
Decreasing by 6% per minute.
Exponential Functions
![Page 33: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/33.jpg)
Example
Problem 2. A quantity can change rapidly. Suppose the initialvalue is 100. Find the formula for the quantity Q at the time tminutes later if Q is:
Increasing by 3 per minute.
Decreasing by 7 per minute.
Increasing by 4% per minute.
Decreasing by 6% per minute.
Exponential Functions
![Page 34: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/34.jpg)
Example
Problem 3. Sales at the stores of company A increase from $2503millions in 1990 to $3699 millions in 1996. Assuming the saleshave been increasing exponentially, find the equation of the salefunction P with respect to t := the number of years since 1990.
P = P0at
P0 = 2503
a6 = 1.478
a = 1.07
Exponential Functions
![Page 35: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/35.jpg)
Example
Problem 3. Sales at the stores of company A increase from $2503millions in 1990 to $3699 millions in 1996. Assuming the saleshave been increasing exponentially, find the equation of the salefunction P with respect to t := the number of years since 1990.
P = P0at
P0 = 2503
a6 = 1.478
a = 1.07
Exponential Functions
![Page 36: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/36.jpg)
Example
Problem 3. Sales at the stores of company A increase from $2503millions in 1990 to $3699 millions in 1996. Assuming the saleshave been increasing exponentially, find the equation of the salefunction P with respect to t := the number of years since 1990.
P = P0at
P0 = 2503
a6 = 1.478
a = 1.07
Exponential Functions
![Page 37: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/37.jpg)
Example
Problem 3. Sales at the stores of company A increase from $2503millions in 1990 to $3699 millions in 1996. Assuming the saleshave been increasing exponentially, find the equation of the salefunction P with respect to t := the number of years since 1990.
P = P0at
P0 = 2503
a6 = 1.478
a = 1.07
Exponential Functions
![Page 38: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/38.jpg)
Recognizing Data
Definition
The values of t and P in a table could from an exponentialfunction P = P0a
t if ratios of P values are constant for equallyspaced t values.
Exponential Functions
![Page 39: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/39.jpg)
Example
Exponential Functions
![Page 40: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/40.jpg)
Families of exponential functions
Exponential Functions
![Page 41: Exponential Functions - University of Nebraska–Lincolntlai3/M119-Section15.pdf · 2016-11-09 · Exponential Functions. Elimination of Drug from the Body Problem 1. When a patient](https://reader034.vdocument.in/reader034/viewer/2022050220/5f663dad0e735a4b413eccfd/html5/thumbnails/41.jpg)
Families of exponential functions
Exponential Functions