Population density on an expanding island is modeled by (people per km )

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

Population density on an expanding island is modeled by

P(A)=3\sqrt{A}+2

(people per km

^2

), where

A

is the island’s area in km

^2

. The area grows according to

A(t)=50+4t^{2}

, with

t

in years. Find

\dfrac{dP}{dt}

when

t=3\text{ yr}

, rounded to the nearest tenth and include appropriate units.