Integrated Math I Name: ________________________________________ Period: ______ Date: _______________

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Exponential Functions

1. Tracy buys a car for $26, 000. The value of the car is expected to decrease by 17% each year. Write a function that can be used to determine f(y), the value of Tracy's car after y years. Justify your answer.

2. A table showing pairs of x– and y–values is shown below. Which equation represents these values?

a. 𝑦 = −4 ∙ 3! b. 𝑦 = 4 ∙ (−3)! c. 𝑦 = −3 ∙ 4! d. 𝑦 = 3 ∙ (−4)!

3. A lake was restocked with native trout. The number of trout increased by the same percent each year, as shown in the graph below. Which equation represents the relationship between y, the number of trout in the lake, and x, the years since the lake was restocked?

a. 𝑦 = 200(0.2)! b. 𝑦 = 200(1.2)! c. 𝑦 = 40𝑥 + 200 d. 𝑦 = 60𝑥 + 200

4. Graph the exponential function 𝑦 = !

! · 2!.

Integrated Math I Name: ________________________________________ Period: ______ Date: _______________

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5. The value of an Internet company is increasing by a constant percentage each year, as shown in the table. Write an expression that gives the company's value in year n. Explain how you found your answer.

6. The mass of a radioactive radium sample remaining after a given number of years is shown in the graph below. Which statements are TRUE? Select all that apply.

A. Half of the initial sample remains after approximately 1,600 years. � B. The initial sample of radioactive radium contains 28 grams. � C. The time-intercept of the radioactive radium sample function is about 10,000 years. D. The amount of radioactive radium approaches 0 grams as time approaches infinity. �

7. An investment has a beginning value of $10,000. The investment is expected to double in value every decade. The function 𝑦 = 10 · 2! represents the value of the investment, in thousands of dollars, after x decades. Create a graph that best represents this function. Ladel axes.

8. Let 𝑓(𝑥) = 8(14)! and 𝑔(𝑥) = 14(8)!. Which statement is TRUE about these functions? (Hint: make a graph or table for both functions given. Then look at how the y-values increase or decrease.)

A. f(x) and g(x) both increase as x increases.

B. f(x) decreases and g(x) increases as x increases.� C. f(x) and g(x) both decrease as x increases. D. f(x) increases and g(x) decreases as x increases.

Integrated Math I Name: ________________________________________ Period: ______ Date: _______________

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9. The radioactive element plutonium 238 (Pu-238) has a half-life of 88 years. This means that the element loses half of its mass every 88 years. A sample of Pu-238 has a mass of N grams today. How do you determine the amount of the sample remaining after 352 years (4 half-lives)?

A. Raise N to the power of 88/352.

B. Multiply N by 88/352 four times.

C. Multiply N by (0.5)!.

D. Raise N to the power !!

!

10. An ant population triples each month. If there are currently 550 ants, what will the ant population be in n months?

A. 550𝑛.

B. 550(3)(n) C. 3 (550!). D. 550(𝑛!).

11. Look at the graph of the exponential function below. Which of these represents the function in the graph?

A. 𝑦 = − !!2 !

B. 𝑦 = −2 !!

!

C. 𝑦 = !

!2 !

D. 𝑦 = 2 !!

!

12. The graph of an exponential function f(x) is shown below. If f(1) = 6, then what is the equation of this function? Show all steps required to derive your equation.

Integrated Math I Name: ________________________________________ Period: ______ Date: _______________

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13. Two investment funds are projected to return 12% and 18% annually through compounding interest. Assume the 12% fund has an initial investment of $150 and the 18% fund a $100 initial investment. Functions representing the value of the two funds are shown. In both functions, t is time in years.

𝑓 𝑡 = 150 (1.12)! 𝑔(𝑡) = 100 (1.18) !

Graph each function over a 10-year period to determine the year in which g(t) surpasses f(t) in value.

Constructed Response DRAFT Criteria For Success

Evidence (Use a table/ equation/ graph/ diagram):

Claim (Answer the question): ____________________________________ _______________________________________________________________________________________________________________________________________________________________________________________ Explanation (Describe in detail how your evidence supports your claim): __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________________________________________________________________________ _____________________________________________________________ _____________________________________________________________

q Highlightimportantinformation.Circlethequestion/prompt.Rephrasethequestion/promptinyourownwords.

1. Restatesthequestion/promptintheirclaim.Claimiscorrect.

2. Providesatleastonepieceofrelevantevidencetosupportclaim.Evidenceiscorrect.

3. Containsacompleteexplanationofhowtheevidencesupportstheclaim.Explanationiscorrect.

4. Paragraphisclearandorganized.Includesatleast2relevantvocabularyterms.

Integrated Math I Name: ________________________________________ Period: ______ Date: _______________

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