Question

A city population, which was initially 15,500, has been dropping by 3% a year. Write an exponential function and graph the function. Use your graph to predict when the population will drop below 8,000.
Could someone help me solve this?

Answer 1

Let be N =8,000., an No =15,500, 
we have  N = No e^ -k.T
k= 3% =3/100
T= periode of time
when T=t, N=No=8,000
so 8000=15,500 e^ -(3/100).t
8000 / 15,500 =e^ -(3/100).t, 0.51 = e^ -(3/100).t, and Ln(0.51) = -3/100.t
implies   t= [100x Ln(0.51)] /3= 22, 04 years

the answer is 22 years and 4 days