AP Calculus ABmediummcq1 pt

A bacteria population is modeled by B(t)=10002t/3B(t)=1000\cdot 2^{t/3}, where tt is in hours. How fast is the population growing when it reaches 4000 bacteria?

A.231231 bacteria/hour
B.924924 bacteria/hour
C.13331333 bacteria/hour
D.27732773 bacteria/hour

Explanation

Core Concept

The population reaches 4000 at t=6t=6 hours. Since B(t)=10002t/3ln23B'(t)=1000\cdot 2^{t/3}\cdot\dfrac{\ln 2}{3}, B(6)=4000ln23924B'(6)=\dfrac{4000\ln 2}{3}\approx 924 bacteria per hour.

Correct Answer

B924924 bacteria/hour

More Unit 4: Contextual Applications of Differentiation practice questions

Try a random question →

Practice more AP Calculus AB questions with full explanations

Practice Unit 4: Contextual Applications of Differentiation Questions →