A town now has a population of 300,000 people and an annual growth rate of 4.5%. If this rate continues, in how many years will the population be more than 500,000 people?

To find out how many years it will take for the population to be more than 500,000 people, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final population
P = the initial population
r = the annual growth rate
n = the number of times interest is compounded per year (we can assume it is compounded annually in this case)
t = the number of years

We can rearrange this formula to solve for t:

t = (log(A/P) / log(1 + r/n)) / n

Given:
P = 300,000
A = 500,000
r = 4.5%
n = 1

Substituting these values into the formula:

t = (log(500,000/300,000) / log(1 + 0.045/1)) / 1

Now, let's calculate it:

t = (log(1.67) / log(1.045)) / 1

Using a calculator, we find that log(1.67) ≈ 0.2231 and log(1.045) ≈ 0.02. Substituting these values into the equation:

t ≈ (0.2231 / 0.02) / 1

t ≈ 11.15

Rounding up to the nearest whole number, it will take approximately 12 years for the population to be more than 500,000 people if the growth rate remains at 4.5%.