The population of a southern city follows the exponential la

The population of a southern city follows the exponential law. If the population doubled in size over 14 months and the current population is 10,000, what will the population be 4 years from now?

The population will be approximately ___ people.

(Do not round until the final answer. Then round to the nearest whole number as needed.)

Solution

current population = 10,000

population doubled in size over 14 months

14 months = 7/6 years

applying exponential growth formula

P = Po e^ kt

plugging the values

20000 = 10,000 e^(7/6k)

dividing both sides by 10000

2 = e^(7/6k)

ln 2 = 7/6 k

k = .5941

population after 4 years

P = 10,000 e^ (.5941 *4 )

P = 107671.518 = 107672 people approximately