Question

An epidemic has hit Clinton City. Its population is declining 22% every hour. In just 4 hours, there are only 35,542 people left in the city. What was the initial population in the city before the epidemic broke out?

Answer 1

35542=p(1-0.22)^4
P=35,542÷(1−0.22)^(4)
P=96,020

Answer 2

`P(4) = 35542`

And we want to find the initial population, if we use the initial condition we have:

`35542= P_o (1-0.22)^4`

And solving for the initial population we got:

[tx] P_o = \frac{35542}{(1-0.22)^4} =96020.387[/tex]

Explanation:

For this case we know that the population is declining 22% every hour.

`r =-0.22`

And we can use the following expression to model the population:

`P(t) = P_o (1+r)^t`

Where P represent the population and t the time in hours

We know the following condition:

`P(4) = 35542`

And we want to find the initial population, if we use the initial condition we have:

`35542= P_o (1-0.22)^4`

And solving for the initial population we got:

`P_o = (35542)/((1-0.22)^4) =96020.387`