A bacterial population covering a circular petri dish of area satisfies

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A bacterial population covering a circular petri dish of area

A\,(\text{mm}^2)

satisfies

P(A)=2000\ln A

. The dish radius grows with time according to

r(t)=50+2t

millimeters, where

t

is measured in hours, and

A=\pi r^{2}

. Compute

\dfrac{dP}{dt}

t=1\text{ h}