Mathematics

Problem

The population density

D

(in hundred animals per square kilometer) of a protected habitat is given by

D(A)=0.5\sqrt{A}

, where

A

is the area of the habitat in square kilometers. The habitat is approximately circular with area

A=\pi R^{2}

, where

R

is its radius in kilometers. When

R=10\text{ km}

, the radius is increasing at a rate of

0.3\text{ km/day}

. What is

\dfrac{dD}{dt}

at that moment (in hundred animals per square kilometer per day)? a)

2.66

0.27

-0.27

0.89