Question

A population of protozoa develops with a constant relative growth rate of 0.7233 per member per day. On day zero the population consists of four members. Find the population size after six days.

Answer 1

307 members

Explanation:

Relative growth rate= Growth rate/population

Given: constant relative growth rate=0.7233

0.7233=
`(dP/dt)/(P)`

`(dP)/(dt) =0.7233 P`

Theorem 2 states that solutions of the differential equation dy/dt = ky are in the form: y(t)=y(0)
`e^k^t`

Writing the soltuion of our dif. equation as:

P(t)=P(0)
`e^(0.7233t)`

since on day zero the population consists of four members.

P(t)=4
`e^(0.7233t)`

next is to find the population size after six days. i.e t=6

P(6)=4
`e^(0.7233* 6)` ≈ 307 members