guided notes (exponential functions)
TRANSCRIPT
Integrated Math-Course 3 Ms. McCullough
Name: _________________________________________ Date: __________________ Hour:__________
GUIDED NOTES: EXPONENTIAL FUNCTIONS
Background Information
In your own words, what is an exponential function?
What does the equation look like?
What does each part of the equation represent?
How do you find the growth/decay rate when given a percentage (r)?
Growth
Decay
**When using the percentage in an equation, I must always remember to change it to a _____________
by moving the decimal ______ places to the ____________.
Graphing
The general graph of an exponential function looks like this…
If a is positive and b is greater than 1, then my graph will look like this…
Integrated Math-Course 3 Ms. McCullough
If a is positive and b is between 0 and 1 (fraction or decimal), then my graph will look like this…
If a is negative and b is greater than 1, then my graph will look like this…
If a is negative and b is between 0 and 1 (fraction or decimal), then my graph will look like this…
Properties of Exponents
=
=
=
Basic Properties of the Graph:
1. All graphs are continuous curves, with no holes or jumps.
2. The x-axis is a horizontal asymptote. Define that!
3. If , then the curve increases as x increases.
4. If , then the curve decreases as x increases.
Integrated Math-Course 3 Ms. McCullough
Growth and Decay Applications
1. In 1982, the population of Somewhere, USA was 380,000. According to the US Census, the
growth rate in that area was approximately .62% each year. Predict the population in the year
2012.
2. Mr. Williams drank a large cup of coffee in the morning. If the caffeine wears off at a rate of 5%
per hour, what percentage is left in his bloodstream after 3 hours?
3. The table below shows the life expectancy (in years) at birth for residents of the United States
from 1970 to 2005. Let x represent the number of years since 1970. Find an exponential
regression model for this data and use it to estimate the life expectancy for a person born in
2015.
Year of Birth 1970 1975 1980 1985 1990 1995 2000 2005
Life Expectancy 70.8 72.6 73.7 74.7 75.4 75.9 76.9 77.7
Example: What amount will an account have after 5 years if $12,000 is invested at an annual rate of 6%
if
a) Compounded weekly?
b) Compounded continuously?
Compound Interest: If a principal P (present value or starting value) is invested at an annual
rate r (written as a decimal) compounded n times a year, then the amount A (future value) in
the account at the end of t years is given by
Continuously Compounded Interest: If a principal P (present value or starting value) is
invested at an annual rate r (written as a decimal) is continuously compounded, then the
amount A (future value) in the account at the end of t years is given by