A laboratory culture contained bacteria at 12:00 hours

MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A laboratory culture contained

5\times10^{3}

bacteria at 12:00 hours. The population grows at a rate proportional to its size. At 16:00 hours the count is

1.5\times10^{4}

. (i) Form the differential equation governing the population

P(t)

(where

t

is the number of hours after 12:00) and obtain the particular function

P(t)

. (ii) How many bacteria will be present at 19:00 hours? (iii) At what time will the population reach

4\times10^{4}

? (Give your answer correct to the nearest minute.)