Question

the number of rainbow smelt in Lake Michigan had an average rate of change of −19.76 per year between 1990 and 2000. The bloater fish population had an average rate of change of −92.57 per year during the same time. If the initial population of rainbow smelt was 227 and the initial population of bloater fish was 1,052, after how many years were the two populations equal?

Answer 1

Initial population of rainbow smelt: 227.
Initial population of bloater fish: 1,052.
t - number of the years;
The equation is:
227 - 19.76 t = 1,052 - 92.57 t
92.57 t - 19.76 t = 1,052 - 227
72.81 t = 825
t = 825 : 72.81
t = 11.33 years = 11 1/3 years = 11 years 4 months
Answer: After 11 years and 4 months.

Answer 2

Answer: For Edgenunity

The linear function that models the population of bloater fish is y2 =

-92.57 x + 1,052

The linear equation that determines when the two populations were equal is

-19.76 x + 227= -92.57x + 1052

The solution is x = 11.33 years