Exponential Function in Context

Jamie's podcast has 1,400 subscribers. The number of her subscribers is increasing at a rate of 5.9% each week. Which function would represent her followers after w weeks?

• y = 1400(1.059)^w

• y = 105.9(1400)^w

• y = 1400(1.59)^w

• y = 1400(5.9)^w

The amount of bacteria in a sample after x hours can be represented by the function y = 200(3)^x. What does (3)^x mean in this context?

• There are 3 bacterium at the beginning

• The bacteria is tripling every hour

• The bacteria is increasing by 3% every hour

• The bacteria is decreasing by 3% every hour

What function is represented by the sequence below? 7, 28, 112, 448 ...

• a_n = 4(7)^n-1

• a_n = 7(4)ⁿ

• a_n = 7(2)^n-1

• a_n = 7(4)^n-1

A guitar that costs $1,600 loses 7% of its value every year. What equation would model the value of the guitar, v, after t years?

• v = 1600(1.07)^t

• t = 1600(.93)^v

• v = 1600(.93)^t

• t = 1600(1.07)^v

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Which of the following is an exponential decay model?

• y = 3 * (1/2)^x

• y = 1/2 * (3)^x

• y = -2 * (2)^x

• y = -3 * (3/2)^x

What is the equation of the graph shown, and what is the y-intercept?

• y = 1⁄3 (3)^x ; a = 1⁄3

• y = 1⁄3 (3)^x ; a = 3

• y = 3 (1/3)^x ; a = 1⁄3

• y = 3 (1/3)^x ; a = 3

The number of subscribers to Francisco's podcast after m months can be modeled by the function y = 150(1.09)^m. What is the growth rate of Francisco's listeners?

• 1.09

• 109%

• 90%

• 9%

The number of subscribers to Francisco's podcast after m months can be modeled by the function y = 150(1.09)^m. How many listeners would Francisco have after one year? (You can't have part of a subscriber)

• 163

• 421.9

• 421

• 163.5

The number of rabbits in Rabbit Forest can be modeled by the function R(x) = a₀(3)^x, where x is the time in years since the rabbits migrated there.

After five years, 1,458 rabbits are in Rabbit Forest. What was the initial population of rabbits?

• 3

• 4

• 5

• 6