The population of a mid western city follows the exponential

The population of a mid western city follows the exponential growth model, n(t) = n_0e^rt. If the population decreased from 1, 500,000 to 1, 200,000 from 1998 to 2001, solve for r and write the exponential formula that models the population. Round r to 3 decimal places. What was the population in 2008? Round your answer to the nearest person.

Solution

n(t) = n_oe^rt

=> 1,200,000 = 1,500,000e^-3r

=> 0.8 = e^-3r

taking ln on both sides, we get:

- ln(0.8) = 3r

=> r = 0.074 or 7.4%

therefore n(t) = n_oe^-0.074t

b] If t is taken from 1998 then t = 10 years

therefore, n(t) = 1500000 e^-0.074(10) = 715670.