AP Precalculus · Question of the Day

AP Precalculus Question of the Day

A fresh daily question to build accuracy, reinforce recall, and turn practice into a steady habit.

Thursday, September 17, 2026

A city has 310,000 residents and grows 1.5% yearly, modeled by $P(t)=310000(1.015)^t$ . Using the information, what is the population after 12 years?

Keep practicing AP Precalculus

Question of the Day

Answer today's AP Precalculus question, reveal the full explanation, then keep the streak going with a new question every day.

A city has 310,000 residents and grows 1.5% yearly, modeled by $P(t)=310000(1.015)^t$ . Using the information, what is the population after 12 years?

$310000(1.15)^{12}$
$310000(1.015)^{12}$ (correct answer)
$310000+0.015(12)$
$310000(1.015)^{11}$

Explanation: This question tests understanding of exponential functions in AP Precalculus, specifically interpreting and calculating exponential growth or decay. Exponential functions model situations where quantities grow or shrink at constant percentage rates. They are represented by y = a * b^x, where a is the initial value, b is the growth/decay factor, and x is time. In this scenario, the city starts with 310,000 residents and grows at 1.5% yearly, so the growth factor is 1.015 (100% + 1.5% = 101.5% = 1.015). Choice B is correct because it accurately applies the exponential formula P(t) = 310000(1.015)^t with t = 12 years, giving us 310000(1.015)^12. Choice A is incorrect because it uses 1.15 as the growth factor, which would represent 15% growth rather than 1.5% growth. To help students: Emphasize careful conversion of percentages to decimals - 1.5% = 0.015, not 0.15. Practice with various percentage values to build accuracy in converting rates to growth factors.