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AP® Calculus AB-BC

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Interpreting Rate of Change in Word Problem

APCALC-NPFNB1

On Bunny Island, there are lots of bunnies. Right now (consider this $t=0$), there are $253$ thousand bunnies on Bunny Island.

Over the next $5$ years, bunnies will die at a rate of $D(t)=10000+5000\sin(2t)$, and bunnies will be born at a rate of $B(t)=15000+10000\cos(2t)$, where both rates are given in number of bunnies per year.

At what rate will the bunny population be changing in $5$ years?

Please round answer to the nearest whole bunny.

A

The population of bunnies is decreasing at a rate of $671$ bunnies per year at the end of $5$ years.

B

The population of bunnies is increasing at a rate of $671$ bunnies per year at the end of $5$ years.

C

The population of bunnies is decreasing at a rate of $670,610$ bunnies per year at the end of $5$ years.

D

The population of bunnies is increasing at a rate of $670,610$ bunnies per year at the end of $5$ years.