The population of a town is 13,000. It decreases at a rate of 5% per year. In about how many years will the population be less than 12,000?

This is an exponential decay problem.

Using the equation Y = a * (1-rate) ^time

where Y is the future value given as 12,000 and a is the starting value given as 13,000.

The rate is also given as 5%.

The equation becomes:

12,000 = 13,000 (1-0.05) ^x

12,000 = 13,000 (0.95) ^x

Divide each side by 13000:

12000/13000 = 0.95^x/13000

12/13 = 0.95^x

Use the natural log function:

x = ln (12/13) / ln (0.95)

x = 1.56 years. (this will equal 12,000

Round to 2 years it will be less than 12000.