Question

The population of a town was 14000 in 2010. If the population decreased at a rate of 1.5% each year thereafter, use an exponential function to find the population after 10 years

Answer 1

To find the population after 10 years, use the exponential function P(10) = 14000(0.985)^10. The population after 10 years is approximately 12,352.

Step-by-step explanation:

To find the population after 10 years, we can use an exponential function. The population of the town in 2010 was 14000. Since the population decreases at a rate of 1.5% each year, the growth factor is 1 - 0.015 = 0.985. We can raise this growth factor to the power of 10 to represent the 10 years, and multiply it by the initial population:

P(10) = 14000(0.985)10

Using a calculator, we can find that P(10) ≈ 12351.745. Therefore, the population after 10 years is approximately 12,352.

Answer 2

12,036

Step-by-step explanation:

If the population was 14000 and it decreased by 1.5%, the new population after a year will be equal to 14000 less the product of 14000 and 1.5%

= 14000 - 1.5% * 14000

= 14000 ( 1 - 0.015)

If the population decreases by 1.5% in the second year, the new population

= 14000 ( 1 - 0.015) - 1.5% * 14000 ( 1 - 0.015)

= 14000 ( 1 - 0.015)(1 -0.015)

= 14000 ( 1 - 0.015)^2

Going by this model, in 10 years, the population would be

= 14000 ( 1 - 0.015)^10

= 12036.23