Help on Precalculus question!!

Question

A population is 25,000 in year t = 0 and grows at a continuous rate of 7.5% per year. Find a formula for P(t), the population in year t

Answer 1

 P(t) = Pe^kt

 

In this case   P(t) = 25000 e^0.075(t)

 

Remember e means the number 2.718 and 0.0075 times t means you have to do the multiplication first and then calulate the value of e elevated to that exponent.

 

You can also see the question this way:

 

First year, P = 25000. Over the course of that year, population grows by 7.5%, that is 1875 individuals.

So,  P(1) = P + Growth P  = P + P (0.075) = 26875

 

Next year, population grows again by 7.5%, which is 2015 individuals.

So P(2) = P(1) + Growth P(1) = P (1+0.075)² =  P (1.075)²

 

 

And so on. That way:

 

P(t) = P (1.075)^t = 25000 (1.075)^t

Answer 2

P(t) = 25000(1.075)^t