Question

The population of a city was 166 thousand at the begining of 2004. The exponential growth rate was 1.5% per year. Use the formula P(t)=P[o]e^(kt) where P[o] is the population in 2004 and k is the exponential growth rate.
a) predict the population in 2016, to the nearest thousand.
b) during which year will the population reach 258 thousand?

Answer 1

I will assume that t is the time in years since 2004

P(t) = 166 e^(.015t)

a)
so for 2016 , t = 12

P(12) = 166 e^(12(.015)) = 166 e^.18 = 198.7 thousand or 199 thousand

b) 258 = 166 e^.015t
1.55422 = e^.015t
.015t = ln 1.55422
t = ln1.55422/.015 = 29.4 years since 2004
or in the year 2033