Which of the following correctly represents the population at time when its rate of…

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

Problem

Which of the following correctly represents the population

P(t)

at time

t

when its rate of change is proportional to its size with constant of proportionality

k

and initial population

P_0

? (a)

P(t)=P_0(1+k t)

(b)

P(t)=P_0 e^{k t}

(c)

P(t)=P_0 e^{-k t}

(d)

P(t)=P_0+k t