Question

A bacteria colony increases in size at a rate of 4.0581e1.6t bacteria per hour. If the initial population is 36 bacteria, find the population four hours later. (Round your answer to the nearest whole number.)

Answer 1

1560

Explanation:

The rate of Increase of the population (P) of the bacteria is given as:

`(dP)/(dt) =4.058e^(1.6t)`

`dP =4.058e^(1.6t)}dt\\Taking\: Integrals\\\int dP =4.058 \int e^(1.6t)dt\\P(t)=(4.058)/(1.6) (e^(1.6t) +K)\\P(t)=2.53625 (e^(1.6t) +K)`

Where k is a constant of Integration.

At t=0, P(t)=36

`36=2.53625 (e^(1.6*0) +K)\\36=2.53625 (e^(0) +K)\\36=2.53625 (1 +K)\\36=2.53625 +2.53625K\\K=13.19`

Therefore:

`P(t)=2.53625 (e^(1.6t) +13.19)\\At \: t=4\\P(4)=2.53625 (e^(1.6*4) +13.19)\\=1559.88\\P(4)=1560`