Exponential Functions Quick Check (Algebra 1 TEKS)

1. Gordon has $395 in credit card debt. If Gordon makes no payments, his debt will increase by 2.5% each month. Which function can be used to find the amount of debt Gordon will have after x months?

• A. f(x) = 395(2.5)ˣ
• B. f(x) = 395(1.25)ˣ
• C. f(x) = 395(1.025)ˣ
• D. f(x) = 395(97.5)ˣ

2. An environmentalist is studying a certain microorganism in a sample of city lake water. The function h(x) = 146(1.16)ˣ gives the number of the microorganisms present in the water sample at the end of x weeks. Which statement is the best interpretation of one of the values of the function?

• F. After 1 week, there will be 146 microorganisms in the water sample.
• G. The initial number of microorganisms in the water sample was 16.
• H. The number of microorganisms decreases by 84% each week.
• J. The number of microorganisms increases by 16% each week.

3. Juan graphed the exponential function, g(x), as shown on the grid. Then, he made 4 statements about the graph. Which of the following statements is NOT true?

• A. The domain of g(x) is x ≥ -3.
• B. The range of g(x) is y > 0.
• C. The function has an asymptote at y = 0.
• D. The function can be represented by g(x) = 8(0.75)ˣ

4. A portion of a neighborhood pond is covered with algae. If left untreated, the algae will grow at an exponential rate. The table below shows the square inches of the pond covered in algae and the number of weeks since the initial patch of algae was discovered. Based on the data, which of the following is the best estimate for the number of square inches of the pond that will be covered with algae after 8 weeks?

• F. 191.5 in²
• G. 266.6 in²
• H. 72.6 in²
• J. 222.2 in²

5. Mrs. Collins wrote the following sequence on the board. Which of the following equations can be used to find the nth term of the sequence?

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6. The graph shows the exponential function h(x). Which function is best represented by the graph?

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7. Which graph best represents f(x) = 2(3)ˣ?

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8. Mr. Hathaway consumes 24,600 milligrams of sodium each week. His doctor suggests that he decrease his sodium consumption by 3% each week to lower his blood pressure. Which function can be used to determined the number of milligrams of sodium Mr. Hathaway can consume after x weeks?

• F. f(x) = 24,600(0.03)ˣ
• G. f(x) = 24,600(0.97)ˣ
• H. f(x) = 24,600(0.7)ˣ
• J. f(x) = 24,600(1.03)ˣ

• A. 12, 15, 18, 21
• B. 36, 108, 324, 972
• C. 3, 12, 36, 108
• D. 12, 36, 108, 324

10. Julian created a graph of the function y = 18.7(4)ˣ. What is the value of the y-intercept of Julian’s graph?