But it doesn't give me the year unless i use 12=1year

Question

The growth in population of a city can be seen using the formula p(t) = 9768e0.003t, where t is the number of years. According to this formula, in how many years will the population reach 14,652? Round to the nearest tenth of a year.

Answer 1

p(t) = 9768e^0.003t,  This is exponential growth; the output p(t) is population t years from now.

 

14,652 =  9768e^0.003t,  We divide by 9768:

 

1.5 = e^.003t     We now take natural logarithms:

 

ln 1.5 =0.003t

 

t = 0.4054651 / 0.003 = 135.155 years

 

Rounding to nearest tenth of a year gives answer 135.2 years (from now, or whenever initial pop. was 9768)