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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?

Respuesta :

Aliwohaish12
35542=p(1-0.22)^4
P=35,542÷(1−0.22)^(4)
P=96,020

Answer:

[tex] P(4) = 35542[/tex]

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

[tex] 35542= P_o (1-0.22)^4[/tex]

And solving for the initial population we got:

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

Step-by-step explanation:

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

[tex] r =-0.22[/tex]

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

[tex] P(t) = P_o (1+r)^t [/tex]

Where P represent the population and t the time in hours

We know the following condition:

[tex] P(4) = 35542[/tex]

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

[tex] 35542= P_o (1-0.22)^4[/tex]

And solving for the initial population we got:

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

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