The population of a town has grown at an annual rate of approximately 2.7%. Determine the following...

Question

The population of a town has grown at an annual rate of approximately 2.7%. How long will it take for its population of 18 450 people to double at this growth rate?

Please be clear and concise! And format your answer neatly. Thank you so much :D

Answer 1

Hi Faatimah, the equation we're going to use here is P(t)=P_i(1+r)^t. In this equation, 'P_i' represents the initial population, 'r' represents the growth rate, 't' represents the amount of time, and 'P(t)' is the new population.

In this case we want to find how long it takes to double our initial population, so our function becomes:

2*18,450 = 18,450(1+2.7%)^t

We can simplify this as:

36,900 = 18,450(1.027)^t

We start by dividing both sides by 18,450. This gives us:

2 = 1.027^t

We're then going to use the natural log (ln) to get rid of the exponent:

t ln(1.027) = ln(2)

Then divide both sides by ln(1.027):

t = ln(2)/ln(1.027)

When we finally calculate our answer, it comes out to be approximately 26. So, in order for our town's population to double when it increases in 2.7% increments, 26 years would need to pass. Hope this helps!