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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? 85,689 14,742 85,688 14,743

Respuesta :

Aliwohaish12
The formula is
P=Ae^(-kt)
P=35542
A initial population ?
E constant
K 0.22
T 4 hours
Solve the formula for A
A=p÷e^(-kt)
A=35,542÷e^(−0.22×4)
A=85,688

Answer:

Step-by-step explanation:

Clinton city was hit by an epidemic and hence population was declining 22% every hour

Let t be the no of hours after epidemic and A, the initial population at the start of epidemic

Then [tex]P(t) = Ae^{-0.22t}[/tex]

Also given that P(4) = 35542

We have to calculate A from this

Substitute t =4 and P (4) = 35542

[tex]P(4) =35542=Ae^-0.22t}[/tex]

[tex]A=35542 e^{.22(4)}\\=85688.15\\=85688[/tex]

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