Culture P begins with 200 bacteria and grows continuously at a rate proportional to…

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

Problem

Culture P begins with 200 bacteria and grows continuously at a rate proportional to its size with growth rate

0.03\text{ h}^{-1}

. Culture Q begins with 120 bacteria and grows continuously with growth rate

0.05\text{ h}^{-1}

. Approximately how many hours after

t=0

will the two cultures contain the same number of bacteria? (a)

17.0\text{ h}

(b)

25.5\text{ h}

(c)

12.8\text{ h}

(d)

34.0\text{ h}