Question

The population of a town was 26,000 in 2015 and 30,000 in 2017. Assuming an exponential model, what is the annual percentage increase in the population?

Answer 1

Answer:

7.4%

Step-by-step explanation:

Answer 2

Answer:

7.4%

Step-by-step explanation:

Exponential growth/decay is modeled as:

A = P(1+r)^t

where A is the final amount, P is the initial amount, r is the rate, and t is time.

If t = 0 represents 2015, and t = 2 represents 2017, then:

26000 = P(1+r)^0

30000 = P(1+r)^2

(1+r)^0 = 1, so P = 26000.  Substituting:

30000 = 26000(1+r)^2

1.154 = (1+r)^2

1.074 = 1+r

r = 0.074

The rate of increase is 7.4%.