Question

Iris has been studying an invasive population of snails. This particular snail has no local predators so the population grows wildly. She has observed that the population follows an exponential rate of growth for fifteen years.
1. Create your own exponential function, f(x), which models the snail population. You will need to identify the principal population of the snails and the rate of growth each year. Explain to Iris how your function shows the principal population and the rate of growth, in complete sentences.

Answer 1

If rate of growth is r (#snail increase/year) and initial population is Po (# of snails), then Population at the end of year, t would be:

P = Po * exp(rt)

where exp is the exponential function. At time t=0, the population is Po. At the end of 1 year, the population has risen to P=Po * exp(r).

You can come up with numbers for Po, r and t and describe what happens at the end of year 1, 2 , 3 etc. How long before the population doubles, quadruples, etc.

Some numbers might be Po = 1,000, r = 0.2, t = 0,1,2 or set P = 2Po to see when the population doubles -- you may find a fraction of a year, which is ok.

Answer 2

thx. can you answer one more? (:

Answer 3

2. A local snail population grows according to the function g(x) = 200(1.03)2x. Demonstrate the steps to convert g(x) into an equivalent function with only x as the exponent. Then explain to Iris how the key features of this local snail population compares to the key features of the invasive population.