Two populations

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

Two populations,

A

and

B

, have identical initial sizes but grow according to

\dfrac{dP}{dt}=kP

with growth constants

k_A

and

k_B

, respectively, where

k_A<k_B

. Let

T_A

and

T_B

denote the times required for each population to double. Which statement is true? (a)

T_A = \dfrac{k_A}{k_B}\,T_B

(b)

T_A<T_B

(c)

T_A>T_B

(d)

T_A-T_B = \ln 2