Question

I need help on the first and last part @Venny

Answer 1

First and last part of what?

Answer 2

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.

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.



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.



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.



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 3

Okay, and exponential function is like this
\(f(x)=a(b)^x\) where a is the starting value and b is the rate of change. To find a rate of growth you pick the percent you want, for example 50% growth, convert it to a decimal by moving the decimal 2 places to the left to get .50 then add that to 1. 1+.50=1.50, so that is an example value of b, or the rate of change.

Answer 4

2 g(x) = 200(1.03)^(2x)
g(x) = 200( 1.03^2 )^x
g(x) = 200( 1.0609 )^x

Answer 5

That can work, but i'm confused to why you put it to the 2x power, you could have just left it as \(g(x)=200(1.03)^x\)

Answer 6

Oh you did the second part

Answer 7

yes

Answer 8

for 3 and 4 how would i put that on a graph?

Answer 9

Well you know the function is increasing because b>1, you can make an x/y table of values close to 0 and plot the points then connect them to make a curve similar to this: http://prntscr.com/44vhem but they are lines so they do not end

Answer 10

I'm confused on how to write it in number form, i can connect it.

Answer 11

For example, ) f(x) = 50(1.27)^x

Answer 12

F(x) is the same as y. If you plug in a value of x you can solve for y

Answer 13

so y=50

Answer 14

If x=0, the y=50 yes

Answer 15

Thank you