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 46,000 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 55,200 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?

Answer 1

To find an exponential model for the frog population, use the formula

, where P0 is the initial population size, e is the base of the natural logarithm, r is the growth rate, and t is the time in years. The exponential model for the frog population is

. Epsilon Delta should order around 49,992 tags for next year's pledge class.

Step-by-step explanation:

To find an exponential model for the frog population, we can use the formula:

Where P(t) is the population size at a given time t, P0 is the initial population size (46,000 frogs), e is the base of the natural logarithm (approximately 2.71828), r is the growth rate, and t is the time in years.

We can find the growth rate by dividing the final population size (55,200 frogs) by the initial population size:

r = ln(P(t)/P0) / t

Plugging in the values, we have:

r = ln(55,200/46,000) / 2 = ln(1.2) / 2 ≈ 0.1823

So, the exponential model for the frog population is:

To find the number of tags Epsilon Delta should order for next year's pledge class, we can substitute t = 1 into the exponential model:

Therefore, Epsilon Delta should order around 49,992 tags for next year's pledge class.