A fish population satisfies

MATHEMATICS · Subjective · AP · Calculus BC · Differential Equations · Differential Equations

Problem

\dfrac{dP}{dt}=kP\!\Bigl(1-\dfrac{P}{3000}\Bigr)

, with

P

measured in fish and

t

in years. Given

P(0)=600

and

P(5)=900

, determine the value of the constant

k

(to three decimal places).