The population P ( in thousands) of Japan from 1980 through 2010 can be modeled by $P = - 15.56 t ^ { 2 } + 802.1 t + 117,001$ where t is the year, with t =0 corresponding to 1980. Determine the population growth rate, $d P / d t$ .
A) $d P / d t = - 31.12 t + 802.1$
B) $d P / d t = 31.12 t + 802.1$
C) $d P / d t = - 31.12 t - 802.1$
D) $d P / d t = 31.12 t - 802.1$
E) $d P / d t = - 31.12 + 802.1 t$

Question

Quizplus · Accepted Answer

The population growth rate, $d P / d t$, is found by differentiating the given equation with respect to $t$. Differentiating $- 15.56 t ^ { 2 } + 802.1 t + 117,001$ gives $- 31.12 t + 802.1$.

The Population P ( in Thousands) of Japan from 1980 P=−15.56t2+802.1t+117,001P = - 15.56 t ^ { 2 } + 802.1 t + 117,001P=−15.56t2+802.1t+117,001

The Population P ( in Thousands) of Japan from 1980 $P = - 15.56 t ^ { 2 } + 802.1 t + 117,001$