Difficult# 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?