Apentix/AP Calculus AB/Unit 7: Differential Equations/Question

AP Calculus ABhardmcq1 pt

A population satisfies $\dfrac{dP}{dt} = kP$ . At $t = 0$ the population is $200$ , and at $t = 6$ it is $800$ . When will the population reach $3200$ ?

A.

12

B.

24

C.

18

D.

9

Explanation

Core Concept

The population quadruples every $6$ time units, and $3200 = 200\cdot 16 = 200\cdot 4^2$ , so two quadrupling periods of $6$ give $t = 12$ .

Correct Answer

A $12$

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