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

Answer:

307 members

Step-by-step explanation:

Relative growth rate= Growth rate/population

Given: constant relative growth rate=0.7233

0.7233=$\frac{dP/dt}{P}$

$\frac{dP}{dt} =0.7233 P$

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$e^{0.7233\times 6}$ ≈ 307 members