Biologists studying an isolated population propose that its rate of change is…

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

Problem

Biologists studying an isolated population propose that its rate of change is proportional both to the current population

P(t)

and to the difference between the carrying capacity

M

and the current population. Which differential equation family, together with an appropriate restriction on

k

, most accurately captures this model? (a)

\dfrac{dP}{dt}=k(M-P)

with

k>0

(b)

\dfrac{dP}{dt}=kP(M-P)

with

k>0

(c)

\dfrac{dP}{dt}=kP(M-P)

with

k<0

(d)

\dfrac{dP}{dt}=kP(P-M)

with

k>0