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?

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Vance

Mathematics

19 July, 21:56

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?

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Paulina Elliott · 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.