Question

Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frog population after x years?

Answer 1

`y=1200(1-0.03)^x\\y=1200(0.97)^x`

y=1200(0.97)^x

Answer 2

y = 1200*0.97^x

where y: frogs population and x: years after the study began

Explanation:

At the beginning the population was 1200 frogs. After the first year (when x = 1) the population was 1200*0.97, that is, 3% less than the previous year. After the second year (when x = 2) the population was 1200*0.97*0.97 = 1200*0.97^2, that is, 3% less than the previous year. It can be seen that for every next years, the population of frogs will be 1200*0.97^x