Exponential Functions
Practice modeling growth, decay, and other exponential relationships.
15 questions
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The function h is defined by h(x) = a x + b, where a and b are positive constants. The graph of y = h(x) in the xy-plane passes through the points (0, 10) and (−2, 325 ⁄ 36 ). What is the value of ab?
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For the function f, f(0) = 86, and for each increase in x by 1, the value of f(x) decreases by 80%. What is the value of f(2)?
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Bacteria are growing in a liquid growth medium. There were 300,000 cells per milliliter during an initial observation. The number of cells per milliliter doubles every 3 hours. How many cells per milliliter will there be 15 hours after the initial observation?
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The equation E(t) = 5(1.8) t gives the estimated number of employees at a restaurant, where t is the number of years since the restaurant opened. Which of the following is the best interpretation of the number 5 in this context?
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Each year, the value of an investment increases by 0.49% of its value the previous year. Which of the following functions best models how the value of the investment changes over time?
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For the exponential function f, the value of f(1) is k, where k is a constant. Which of the following equivalent forms of the function f shows the value of k as the coefficient or the base?
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A model estimates that at the end of each year from 2015 to 2020, the number of squirrels in a population was 150% more than the number of squirrels in the population at the end of the previous year. The model estimates that at the end of 2016, there were 180 squirrels in the population. Which of the following equations represents this model, where n is the estimated number of squirrels in the population t years after the end of 2015 and t ≤ 5?
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The table shows selected values from function f. x f(x) −1 16 0 17 1 18 2 19 Which of the following is the best description of function f ?
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P(t) = 260(1.04) ( 6 ⁄ 4 )t The function P models the population, in thousands, of a certain city t years after 2003. According to the model, the population is predicted to increase by 4% every n months. What is the value of n ?
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x, 2x, 4x, . . . The first term in the sequence above is x , and each term thereafter is equal to twice the previous term. Which of the following is the sum of the first five terms of this sequence?
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Each term in the sequence below is –2 times the previous term. What is the seventh term of the sequence?
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Each term in the sequence below is 2 ⁄ 3 times the previous term. What is the seventh term of the sequence?
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Each term in the sequence below is five times the previous term. What is the 20th term of the sequence?
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Each term in the sequence below is –4 times the previous term. What is the value of xy?
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Each term in the sequence below is three times the previous term. What is the product of the 100th and 101st terms of the sequence?
Hard