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.

Answer 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.

15 years when x is equal to the time unit. So 15 is equal to x.
We don’t have P so let’s have 150 as P and let’s say that the rate doubles each year so we will have .5.

P = amount you start with
R = rate
X = time

f(x) = p(1 + r)^x
f(15) = 150(1 + 0.5)^15
f(15) = 150(1.5)^15
f(15) = 150(437.893890380859)
f(15) = 65684.0835571288 (round to 65,684) This will be the snail population in 15 years. The solution is irrational.


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.

g(x) = 200(1.03)^2x
g(x) = 200(1.03^2)^x
g(x) = 200(1.0609)^x
g(x) = 212.18 (round to 212) This solution is irrational.

Both solutions for the local and invasive are irrational and the invasive population is 65,472 more than the local population.


Iris wants to graph the invasive snail population to show the city council. Justify what the appropriate domain and range would be for the function f(x), what the y-intercept would be, and if the function is increasing or decreasing.

Answer 2

@satellite73 is this correct?

Answer 3

yes

Answer 4

I need help with the third part though