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AP® Calculus AB-BC

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Estimating from a Table: Reasonable Population

APCALC-SSLJ4V

On People Island, there are a lot of people. Specifically, at time $t=0$, there are 150 thousand people. Over the next 63 years, the number of people on the island is represented by the twice differentiable function $P(t)$ on the interval $0 \le t\le 63$, where $P(t)$ is measured in thousands of people and $t$ is measured in years. Some specific data about the population is given by the table below:

$t$ 0 25 41 54 63
$P'$ 0 2 5 6 7



Because People Island is a desirable place to be, the rate that the population changes increases from $0\le t\le 63$. Which of the following is a reasonable number of people to inhabit People Island after 63 years?

A

$173\text{ people}$

B

$412\text{ people}$

C

$201,000\text{ people}$

D

$332,587\text{ people}$