lesson 10.1 assignment 10.1 assignment name date small investment, big reward exponential functions...

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Chapter 10 Assignments 139

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Lesson 10.1 Assignment

Name Date

Small Investment, Big RewardExponential Functions

1. Wildlife biologists are studying the coyote populations on 2 wildlife preserves to better understand the role climate plays in population change. The table displays the coyote populations on both preserves for each year of the study. The Year 0 corresponds to the date of the biologists’ initial observations at the start of their study.

Year AlaskaPreserve TennesseePreserve

0 200 80

1 220 100

2 242 125

3

4

a. Do the populations represent arithmetic or geometric sequences? Explain your reasoning.

b. For each wildlife preserve, write a sequence to represent the coyote population in a given year.

c. For each wildlife preserve, write a function to represent the coyote population as a function of the year of the study.

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140 Chapter 10 Assignments

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d. Use the functions you wrote in part (c) to complete the table. Round all answers to the nearest whole number.

e. Graph and label the functions you wrote in part (c).

x

200

210 43

y

400

65Year of Study

87 9

600

800

900

100

300

500

Coy

ote

Pop

ulat

ion

700

f. Do the populations represent examples of exponential decay, exponential growth, or neither? Explain your reasoning.

g. Will the coyote population on the Tennessee preserve ever exceed the coyote population on the Alaska preserve? If so, when will this occur?

h. Make a hypothesis about the role the climate plays on coyote populations based on the results of the study, assuming all other population growth factors are equal. Explain your reasoning.

Lesson 10.1 Assignment page 2

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We Have Liftoff!Properties of Exponential Graphs

1. Caleb wants to invest $1000 in a savings account. Lincoln Federal Bank is offering 6% interest compounded yearly. Washington National Bank is offering 5.5% interest compounded daily.

a. For each bank, write an exponential function to represent the amount of money Caleb would have in the account after t years.

b. Determine which bank Caleb should choose if he plans to invest his money for 5 years. If Caleb decides to leave the money in the bank for a longer period of time, will the other bank be a better deal in the long run? Explain your reasoning.

c. Complete the table for the 2 functions you wrote in part (a). Summarize the characteristics in terms of the problem situation.

LincolnFederalBank WashingtonNationalBank

Domain

Range

Intercepts

RightEndBehavior

IntervalsofIncreaseorDecrease


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2. In 2010, Bolivia had a population of 10.5 million people and an annual growth rate of 1.6%.

a. Write a function to model Bolivia’s population with respect to t, the number of years since 2010. Write your function in the form N(t) 5 N0 e rt.

b. Use your model to predict what Bolivia’s population will be in the year 2030.

c. Use your model to estimate Bolivia’s population in the years 1990 and 1970.

d. Use a graphing calculator to estimate when Bolivia’s population will reach 20 million people.

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e. Discuss the domain, range, asymptotes, intercepts, end behavior, and intervals of increase and decrease for your population model as they relate to the problem situation.


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I Like to Move ItTransformations of Exponential Functions

1. Given: f(x) 5 2 x and g(x) 5 f( 1 __ 3 x ) . The graph of f(x) is shown.

x

2

4

2242024 22 8628 26

y

24

26

28

6

8 f(x)

a. Complete the y-values for each of the reference points on f(x) in the table.

ReferencePointsonf(x) CorrespondingPointsong(x)

(21, )(0, )

(1, )

b. Complete the table in part (a) to determine the points on g(x) that correspond to each of the reference points on f(x).

c. Sketch and label the graph of g(x) on the coordinate plane.


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d. Describe the transformation on the graph of f(x) that produces g(x).

e. Write g(x) as an exponential function.

f. Describe the effect the transformation had on the domain, range, asymptotes, intercepts, end behaviors, and intervals of increase and decrease. Explain your reasoning.

2. Given: p(x) 5 5 x and t(x) 5 p(2x) 24.

a. Describe the transformation on the graph of p(x) that produces t(x).

b. Write t(x) as an exponential function.

3. Given: m(x) 5 1.5 x and k(x) 5 1 __ 3 m(2x).

a. Describe the transformation on the graph of m(x) that produces k(x).

b. Write k(x) as an exponential function.

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I Feel the Earth MoveLogarithmic Functions

1. Given: f(x) 5 3 x.

a. Write the function f 21 (x), the inverse of f(x) 5 3 x.

b. Graph and label the functions f(x) and f 21 (x) on the coordinate plane.

x

2

4

2242024 22 8628 26

y

24

26

28

6

8

c. Describe how to calculate f 21 (3) without a calculator. Then, calculate f 21 (3), f 21 (9), and f 21 (27).

d. Determine the domain, range, asymptotes, intercepts, end behavior, and intervals of increase and decrease for f 21 (x).


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2. The loudness of sounds is measured in decibels (dB). The loudness, L, of a sound is a function of its

intensity, I, and can be determined using the function L(I ) 5 10 log ( I __ I0

) , where both I and I0 are

measured in watts per square meter (W/ m 2 ). In the function, I0 represents a barely audible sound or “threshold sound” and is equal to 10 212 W/ m 2 .

a. The Guinness World Record for the Loudest Crowd Roar at an Outdoor Stadium was set during an NFL game in Seattle. The roar measured 136.6 dB. During an NFL game in Kansas City, the roar of the crowd was measured at 133.1 dB. How many times more intense was the roar at the Seattle game?

b. The fans in Kansas City attempted to break the Guinness World Record for the Loudest Crowd Roar. Their goal was to create a roar that was 2 times as intense as the Seattle roar. In order for the fans in Kansas City to be successful, how many decibels did their roar need to be?

c. In fact, the fans in Kansas City successfully recorded a new record of 140 dB. Determine the intensity of the roar.

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More Than Meets the EyeTransformations of Logarithmic Functions

1. Consider the function g(x), which is formed by translating the function f(x) 5 log2 x left 3 units and up 4 units.

a. Write g(x) in terms of f(x).

b. Complete the table by determining the corresponding point on g(x) for each reference point on f(x).

ReferencePointonf(x) CorrespondingPointong(x)

(0.5, 21)

(1, 0)

(2, 1)

(4, 2)

c. Graph and label g(x).

x

2

4

2242024 22 8628 26

y

24

26

28

6

8

f(x)

d. Write g(x) as a logarithmic function.

e. List the domain, range, and any asymptotes of the logarithmic function g(x).


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2. Consider p(x) 5 2 x __ 3

, which is a transformation of the function f(x) 5 2 x .

a. Describe the transformation(s) on the graph of f(x) to produce p(x).

b. Write the equations of the inverse functions f 21 (x) and p 21 (x).

c. Describe the transformation(s) on the graph of f 21 (x) to produce p 21 (x).

d. Graph and label the inverse function p 21 (x).

x

2

4

2242024 22 8628 26

y

24

26

28

6

8

lesson 10.1 assignment 10.1 assignment name date small investment, big reward exponential functions...

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