Exponential Question??

Question

The population of a southern city follows the exponential law. If the population doubled in size over 30 months and the current population is 50,000 , what will the population be 3 years from now?

I am so confused.

How do I do this step by step and put it into my calculator? Many thanks!

Answer 1

An exponential increase can be mathematically defined by the equation:

P_c = e^kt * P_o , where  P_c is the current or projected population, P_o is the original population, and k is a constant.

It is given that t = 30 months, and that P_c = 2* P_o. From that, we can solve for k:

P_c = e^kt * P_o

2 * P_o = e^30k * P_o

2 = e^30k

ln(2) = 30k

k = ln(2)/30 = 0.0231

Plugging k=0.0231 and t = 36 into the equation to get the population, P_c , 3 years (36 months) in the future gives:

P_c = e^(0.0231*36) * 50000

    = 114,850