Solve the problem.
-The size of a population of mice after $t$ months is $\mathrm { P } = 100 \left( 1 + 0.2 t + 0.02 t ^ { 2 } \right)$. Find the growth rate at $t = 23$ months.
A) $112 \mathrm { mice } / \mathrm { month }$
B) $56 \mathrm { mice } / \mathrm { month }$
C) $224 \mathrm { mice } / \mathrm { month }$
D) $212 \mathrm { mice } / \mathrm { month }$

Question

Quizplus · Accepted Answer

To find the growth rate at $t = 23$ months, we need to differentiate the given function with respect to $t$ and then substitute $t = 23$. The derivative of $P$ with respect to $t$ is $P' = 100(0.2 + 0.04t)$. Substituting $t = 23$ gives $P' = 100(0.2 + 0.04 \times 23) = 100(0.2 + 0.92) = 100 \times 1.12 = 112$ mice/month.

Solve the Problem ttt Months Is P=100(1+0.2t+0.02t2)\mathrm { P } = 100 \left( 1 + 0.2 t + 0.02 t ^ { 2 } \right)P=100(1+0.2t+0.02t2)

Solve the Problem $t$ Months Is $\mathrm { P } = 100 \left( 1 + 0.2 t + 0.02 t ^ { 2 } \right)$