A microbiology laboratory models the population of a bacterial culture (measured in…

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A microbiology laboratory models the population

P

of a bacterial culture (measured in thousands of cells) by

P(t)=120t^{3/2},

where

t

is the time in hours since the culture was initiated and

0\le t\le 30

. (a) Determine

P'(t)

and state its units. (b) Calculate the instantaneous growth rate of the population at

t=16

hours. (c) Using the result from part (b), approximate the change in the bacterial population during the first

0.10

hour after

t=16

. (d) Explain, in practical terms, what the exponent

\tfrac{3}{2}

suggests about how the per-hour growth rate behaves as the culture ages.