The population of a southern city follows the exponential la

The population of a southern city follows the exponential law. If the population doubted in size over 30 months and the current population is 90.000. what will the population be 3 years from now? What wilt the population be 3 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

Let P be the size of the population a any point of time \'t\' .

Now, let the monthly growth rate is b.

So, at any \'t+k\'-th month the population will be, P\' = P*b^{(t+k - t )} = P*b^k , for all k = 0,1,2,...

Now, we know that for k = 30 months , P\' = 2P

=> 2P = P*b³⁰

=> b = 2^1/30 = 1.023374 .

Now at present P = 90000. After 3 years = 36 months it will be ,

(90000)*(1.023374)³⁶ = 206766.5 = 206767 approximately .