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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?

A.) 14,742

B.) 85,688

C.) 14,743

Verified Answer :

I'm not positive of this answer but, I'm pretty sure it's 85,688 using common sense. The population would definitely be greater before the epidemic hit because, and infectious disease or anything like that would obviously cause the population to decrease. Therefore, B) is the most reasonable answer.

JeanaShupp

Answer: B.) 85,688

Step-by-step explanation:

The exponential decay equation is given by :-

\(y=Ae^{-rt}\), where A is the initial amount , r is the rate of decay and t is time period.

Given : Rate of decay for every hour: \(r=22\%=0.22\)

Time period : \(t=4\)

Put y = 35,542 , r = 0.22 and t=4 in the above equation , we get

\(35,542=Ae^{-0.22\times4}\\\\\Rightarrow\ 35,542=A(0.414782911682)\\\\\Rightarrow\ A=\dfrac{35542}{0.414782911682}=85688.1973654\approx85,688\)

Hence, the initial population in the city before the epidemic broke out =85,688

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