Mathematics

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.