For the logistic model with

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

Problem

For the logistic model

\dfrac{dN}{dt}=kN(M-N)

with

k,M>0

, which of the following best describes when the growth rate

\dfrac{dN}{dt}

is largest as the population

N

increases from

0

M

? (a) When

N

is very close to

M

(b) When

N

is about one–half of

M

N

is very close to

0

(d) When

N

is about one–quarter of

M