Frogs have been breeding like flies at the Enormous State University (ESU) campu

Question

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 (t = 0) they managed to tag all 54,000 of them (with little Epsilon Delta Fraternity tags). This year's pledge class discovered that all the tags had all fallen off, and they wound up tagging a total of 81,000 frogs.
(a) Find an exponential model for the frog population.



f(t) =





(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?
f(t) =

Explanation / Answer

a)For t = 0, a =  54,000.
f = 54,000kt
for t=1 we need f = 81,000
81,000 = 54,000k1
k = 1.5

The model is: f = 54,000*1.5t

b) t=2
f = 54,000(1.5)²
= 121,500

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