A microbiologist begins an experiment at time (measured in hours)

MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

A microbiologist begins an experiment at time

t=0

(measured in hours). The number of bacteria in the culture is modeled by

P(t)=P_0e^{kt}

, where

k

is known to be

0.45\text{ hr}^{-1}

. After

3

hours, the population is measured to be

1.60\times10^{6}

cells. (a) Write an explicit formula for

P(t)

in terms of

P_0

. (b) Determine the initial population

P_0

present at the start of the experiment. (c) Interpret your result from part (b) in the context of the experiment.