Answer:
B) 69,726
Step-by-step explanation:
We have been given that an epidemic has hit Minecole City. Its population is declining 34% every hour.
As population of the city declining 34% per hour, this means that population is decreasing exponentially.
Since we know that an exponential function for continuous growth is in form: [tex]y=a*e^{kt}[/tex], where,
[tex]a=\text{Initial value}[/tex],
[tex]e=\text{Mathematical constant}[/tex],
[tex]k=\text{Continuous growth rate}[/tex] If k>0 then amount is increasing, if k<0 then amount is decreasing.
Let us convert our given rate in decimal form.
[tex]34\%=\frac{34}{100}=0.34[/tex]
Upon substituting k=-0.34 in exponential decay function we will get,
[tex]y=a*e^{-0.34t}[/tex]
Therefore, the function [tex]y=a*e^{-0.34t}[/tex] represents the population of city after t hours.
As we have been given that in 3 hours there are only 25,143 people left in the city, so to find our initial value we will substitute y=25143 and t=3 in our function.
[tex]25143=a*e^{-0.34*3}[/tex]
[tex]25143=a*e^{-1.02}[/tex]
[tex]25143=a*0.3605949401730783[/tex]
Let us divide both sides of our equation by 0.3605949401730783.
[tex]\frac{25143}{0.3605949401730783}=\frac{a*0.3605949401730783}{0.3605949401730783}[/tex]
[tex]69726.43595=a[/tex]
[tex]a\approx 69726[/tex]
Therefore, the initial population in the city before the epidemic broke out was 69726 and option B is the correct choice.
