SAT question 5c00c2c1 (Nonlinear Functions)

Question

There were no jackrabbits in Australia before $1788$ when $24$ jackrabbits were introduced. By $1920$ the population of jackrabbits had reached $10$ billion. If the population had grown exponentially, this would correspond to a $16.2%$ increase, on average, in the population each year. Which of the following functions best models the population $p (t)$ of jackrabbits $t$ years after $1788$ ?

95

Difficulty:Medium

A

$p (t) = 1.162 (24)^{t}$

B

$p (t) = 24 (2)^{1.162 t}$

C

$p (t) = 24 (1.162)^{t}$

D

$p (t) = (24 \cdot 1.162)^{t}$

College Board · Accepted Answer

The correct answer is C. Choice C is correct. This exponential growth model can be written in the form p(t) = A (1 + r)^t , where p(t) is the population t years after 1788 , A is the initial population, and r is the yearly growth rate, expressed as a decimal. Since there were 24 jackrabbits in Australia in 1788 , A = 24 . Since the number of jackrabbits increased by an average of 16.2% each year, r = 0.162 . Therefore, the equation that best models this situation is p(t) = 24(1.162)^t . Choices A, B, and D are incorrect and may result from misinterpreting the form of an exponential growth model.

CookSAT · Answer

Note: The initial population is 24, and a 16.2% yearly increase multiplies it by 1.162 each year.

Explanation

Enter in Desmos:

Why the other choices are wrong

SAT Question 5c00c2c1: Nonlinear Functions answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong