Section 2.2 (77) Frogs have been breeding like flies at the Enormous State University (ESU) campus! Each year, the pledge class of the Epsilon Delta fraternity is instructed to tag all the frogs residing on the ESU campus. Two years ago, they managed to tag all 50,000  of them (with little Epsilon Delta Fraternity tags). This year’s pledge class discovered that last year’s tags had all fallen off, and they wound up tagging a total of  75,000 frogs.a)Find an exponential model for the frog population.b)Assuming exponential population growth and that all this year’s tags have fallen off, how many tags should Epsilon Delta order for next year’s pledge class?

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Asked Dec 12, 2019
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Section 2.2 (77) 

Frogs have been breeding like flies at the Enormous State University (ESU) campus! Each year, the pledge class of the Epsilon Delta fraternity is instructed to tag all the frogs residing on the ESU campus. Two years ago, they managed to tag all 50,000  of them (with little Epsilon Delta Fraternity tags). This year’s pledge class discovered that last year’s tags had all fallen off, and they wound up tagging a total of  75,000 frogs.

a)Find an exponential model for the frog population.

b)Assuming exponential population growth and that all this year’s tags have fallen off, how many tags should Epsilon Delta order for next year’s pledge class?

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Expert Answer

Step 1

(a)

 

Let the general exponential equation for rate of increase in frogs’ population be given as,

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P = Ab' P = population of frogs A,b = constant t = time in years

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Step 2

Considering given condition of frog population 2 years ago as the initial value an...

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P = Ab' initial condition: t = 0 P = 50000 50000 = Ab° A = 50000 After 2 years (present): t= 2 P= 75000 75000 = 50000 -6² b = 1.5 Thus equation formed is: P= 50000-(JI.5)

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