Question

Help please!!<3
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. 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.

Answer 1

2. 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.

3. In five years, a garden festival plans on using the park where Iris has been studying the invasive snails. Explain to the garden festival committee how to find the average rate of change for the snail population between years 2 and 5. Describe what this average rate of change represents.

Answer 2

1. What you've written is equivalent to 200·1.03·2·x.
If the 2x is an exponent, it should be indicated with a ^ and parentheses: 200·1.03^(2x).

1.03²ˣ = (1.03²)ˣ = 1.0609ˣ

g(x) = 200·1.0609ˣ

Answer 3

@LeoRay
I still don't think I quite understand...

Answer 4

Can someone please help??? D:

Answer 5

This: \[A^{2x}\] can be written as
\[({A^2})^{x}\]