Question #5c00c2c1 - SAT Suite Question Bank

ID: 5c00c2c1

Modded SAT Question Bank by Abdullah Mallik

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 $p of t$ of jackrabbits t years after 1788?

$p of t equals, 1 point 1 6 2 times, 24 raised to the t power$
$p of t equals, 24 times, 2 raised to the 1 point 1 6 2, t power$
$p of t equals, 24 times, 1 point 1 6 2 raised to the t power$
$p of t equals, open parenthesis, 24 times 1 point 1 6 2, close parenthesis, raised to the t power$

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Correct Answer: C

Rationale

Choice C is correct. This exponential growth model can be written in the form $p of t equals, A, times, open parenthesis, 1 plus r, close parenthesis, raised to the t power$ , where $p of t$ 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, $A, equals 24$ . Since the number of jackrabbits increased by an average of 16.2% each year, $r equals 0 point 1 6 2$ . Therefore, the equation that best models this situation is $p of t equals, 24 times, 1 point 1 6 2 raised to the t power$ .

Choices A, B, and D are incorrect and may result from misinterpreting the form of an exponential growth model.

Question Difficulty: Medium