The population of insects in a laboratory experiment is incr

The population of insects in a laboratory experiment is increasing according to the formula P(t) = 450 (squareroot 3)^1/6, where t is measured in weeks, P in number of insects. How long will it take for the population to triple? Find the growth factor and weekly percentage growth rate.

Solution

given P(t)=450(3)^t/6

a)initial population =450

triple population = 450*3

450*3=450(3)^t/6

(3)^t/6=3

(3^1/2)^t/6=3

3^t/12=3

t_/12 =1

t =12

it takes 12 weeks for population to triple

b)P(t)=450(3^1/6)^t

P(t)=450(1.09587)^t

gowth factor =1.0959

growth rate=1.0959-1=0.0959

percentage growth rate =9.59%