Question

The population of a town is 20,000. It decreases at a rate of 9% per year. In about how many years will the population be fewer than 14,000?
a. 1 year
b. 2 years
c. 3 years
d. 4 years​

Answer 1

Answer:

d. 4 years

Step-by-step explanation:

20000(.91^t) < 14000

0.91^t < 0.7

t × ln(0.91) < ln(0.7)

t > ln(0.7) ÷ ln(0.91)

t > 3.782

t = 4

Answer 2

Answer:

  d.  4 years

Step-by-step explanation:

A graphing calculator can be a real help with problems like this.

Or, you can write an explicit formula for the population and solve for the time it takes.

  p = p0(1 +r)^t = 20,000(0.91^t) . . . . . . for r = -0.09, p0 = 20,000

Fill in p=14000, and divide by 20,000.

  14000/20000 = 0.91^t

Take logarithms.

  log(14/20) = t·log(0.91)

  log(0.7)/log(0.91) = t ≈ 3.782

In 4 years, the town's population will be fewer than 14,000.