The Florida scrub jay, a native bird of North America, is in danger of becoming extinct. In the year 2000, there were 580 Florida scrub jays in the Oscar Schere State Park, and every year since the population of the endangered bird has decreased by 27. If y is the number of years since 2000 and f (y) is the population of Florida scrub jays in the park y years after 2000, then this situation is modeled by the function f (y) = - 27y + 580. If park rangers count a population of 418 at the end of a specific year, how many years have passed since 2000 at the time of counting? Enter your solution in the space provided.

Question

Mathematics

Annie Shelton

6 August, 17:02

The Florida scrub jay, a native bird of North America, is in danger of becoming extinct. In the year 2000, there were 580 Florida scrub jays in the Oscar Schere State Park, and every year since the population of the endangered bird has decreased by 27. If y is the number of years since 2000 and f (y) is the population of Florida scrub jays in the park y years after 2000, then this situation is modeled by the function f (y) = - 27y + 580. If park rangers count a population of 418 at the end of a specific year, how many years have passed since 2000 at the time of counting? Enter your solution in the space provided.

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Answers (1)

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Margaret Chase · Answer 1

6 years have passed since 2000.

Plugging in the population at the time of counting we have

418 = - 27y + 580

Subtract 580 from both sides:

418 - 580 = - 27y + 580 - 580

-162 = - 27y

Divide both sides by - 27:

-162/-27 = - 27y/-27

6 = y