P(t)=184,000e−0.012t, where t is the number of years from the present. What does this model predict the population will be in 6 years?

Question

The population of a certain inner-city area is estimated to be declining according to the model , where is the number of years from the present. What does this model predict the population will be in 6 years? Round to the nearest person.

Answer 1

.012t = .012(6) = .072

e^-0.72 = about 1/1.07466= about 0.930530895

184000(.930530895) = 171,177 people in 6 years, rounding off to nearest integer, although that last person is either partly dead or on his way to leave the city.

Answer 2

P(t)=184000e^-0.012t

P(6) = 184000e^-0.012(6) = 184000(0.930531) ≈ 171218 people