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

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.

3)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.

4)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

@undeadknight26

Answer 3

@tkhunny

Answer 4

Not sure where you are stuck. Clues?

Answer 5

i need help working through these set of questions,been stuck on this assignment for quite a while now.

Answer 6

NonResponsive. You must have some idea about some of it. Where are you struggling?

Answer 7

1) You will need to identify the principal population of the snails and
2) The rate of growth each year.

What are these?

Answer 8

we need to make them up,correct?

Answer 9

the population follows an exponential rate of growth for fifteen years

Answer 10

Okay, so

\(P_{0} = Initial\;Population\)
\(G = Annual\;Growth\;Rate\)

\(P(t) = P_{0}(1+G)^{t}\;for\;t\in (0,15)\)

Is there some part of this that is not familiar?

Answer 11

looks familiar

Answer 12

Okay, i did ALL of that. It is time for you to show some of your work.

\(200\cdot(1.03)^{2x} = 200\cdot What^{x}\)

It's just an algebra problem. It has nothing to do with snails.

Answer 13

well when i plug in \[200*(1.03)^{2x}\] i get \[212.18\]

Answer 14

1) Never say or do "plug in". It doesn't exist.
2) What are you substituting and why are you doing that?
3) It has absolutely NOTHING to do with the 200.

Your task is to rewrite: \(1.03^{2x} = What^{x}\)

Answer 15

i honestly have no idea,which is the reason why i'm failing algerbra :/.

Answer 16

Well, you will have to try harder. You showed virtually none of your own work on this thread. Doing it. Trying it. Finding a way to succeed. That's how you don't fail algebra.

Answer 17

\[1.03^{2x}=1.0609^{x}\]

Answer 18

\(P_{0} = Initial\;Population\)
\(G=Annual\;Growth\;Rate = 0.0609\)

\(P(t)=P_{0}\cdot (1+G)^{t}\;for\;t∈(0,15)\)

Okay, now identify the principal parts and explain how this answers the demands of the problem statement.

Answer 19

by Principal parts are referring to the Initial Population?

Answer 20

And the growth rate. good work.

Answer 21

So are we suppose to make-up our own Initial Population?

Answer 22

That is not necessary. \(P_{0}\) is find. When we know the beginning population for a particular case, that's where we'll put it.