Question

A population of protozoa develops with a constant relative growth rate of 0.8329 per member per day. On day zero the population consists of six members. Find the population size after four days. (Round your answer to the nearest whole number.)

Answer 1

Answer:

The population size after four days is calculated as 168.

Step-by-step explanation:

Let the population size be P

 t be the time variable which is measured in hours

Therefore,

by the differential equation    

$\frac{dp}{dt}$= 0.8329P

So,by solving and expifying the equation on both sides, we get

P = Ae^0.8329t

Therefore,from the first equation we get

P(0) = 6,  

A = 6.

Therefore the population size after four days is

P(4) =${6}\times{e^0.8329(4)}$

= 168( rounded to nearest whole number)