Question

A population of bacteria doubles every 5 hours. If the initial size of the population is 1 (measured in millions). (a) Find the formula for the population P (t) after t hours. (b) What is the population after 15 hours? (c) When will the population reach 10 (measured in millions)?

Answer 1

Given,

Doubling rate =5 hours

Initial Population=1(in million)

a)The equation for the population is:

$P(t)=1*2^{\frac{t}5}$​​​​​​

b)Population after 15 hours =$P(15)=1*2^{\frac{15}5}=2^3=8$(in million).

c)$10=1*2^{\frac{t}5}$

$log 10={\frac{t}5}=\frac{t}{5}log2=\frac{0.301t}{5}=1$

$t=\frac{5}{0.301}\simeq16.61$

The population will reach 10(in million) after 16.61 hours .