Which of the following best describes the roles of the parameters and in the…

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

Problem

Which of the following best describes the roles of the parameters

L

and

k

in the differential equation

\dfrac{dy}{dt}=k y\left(1-\dfrac{y}{L}\right)

modeling population growth? (a)

L

is the initial population size, while

k

is the carrying capacity that the population approaches. (b) Both

L

and

k

are growth–rate constants;

L

scales the quadratic term and

k

scales the linear term in the model. (c)

L

is the limiting population size (carrying capacity), and

k

is the intrinsic growth rate that determines how quickly the population approaches

L

. (d)

L

represents the intrinsic growth rate, whereas

k

gives the limiting population size.