Question #b73ee6cf - SAT Suite Question Bank

ID: b73ee6cf

Modded SAT Question Bank by Abdullah Mallik

The population of a town is currently 50,000, and the population is estimated to increase each year by 3% from the previous year. Which of the following equations can be used to estimate the number of years, t, it will take for the population of the town to reach 60,000 ?

$50,000 equals, 60,000 times, open parenthesis, 0 point 0 3, close parenthesis, to the power t$
$50,000 equals, 60,000 times, open parenthesis, 3, close parenthesis, to the power t$
$60,000 equals, 50,000 times, open parenthesis, 0 point 0 3, close parenthesis, to the power t$
$60,000 equals, 50,000 times, open parenthesis, 1 point 0 3, close parenthesis, to the power t$

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Correct Answer: D

Rationale

Choice D is correct. Stating that the population will increase each year by 3% from the previous year is equivalent to saying that the population each year will be 103% of the population the year before. Since the initial population is 50,000, the population after t years is given by 50,000(1.03)^t. It follows that the equation 60,000 = 50,000(1.03)^t can be used to estimate the number of years it will take for the population to reach 60,000.

Choice A is incorrect. This equation models how long it will take the population to decrease from 60,000 to 50,000, which is impossible given the growth factor. Choice B is incorrect and may result from misinterpreting a 3% growth as growth by a factor of 3. Additionally, this equation attempts to model how long it will take the population to decrease from 60,000 to 50,000. Choice C is incorrect and may result from misunderstanding how to model percent growth by multiplying the initial amount by a factor greater than 1.

Question Difficulty: Hard