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.
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.

- JozelynW

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- schrodinger

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- JozelynW

@pooja195 please help me

- anonymous

\[g(x)=200(1.03)^{2x}=200(1.03^2)^x\]
Growth rate formula
\[g(x)=A(1+r)^x\]
A = initial amount, r = growth rate

- JozelynW

the answer is g(x)=200(1.0609)^x. I need help with the second part of the question @peachpi

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## More answers

- JozelynW

@dan815

- JozelynW

@readergirl12

- JozelynW

@avis

- anonymous

|dw:1433023159625:dw|

- JozelynW

@peachpi Then explain to Iris...... how do i do that part?

- JozelynW

@mathmate

- JozelynW

do you know

- mathmate

Use the identity \(b^{kx} =b^kb^x \)
Since b=1.03, b^2=1.03^2=1.0609
For the rest, see explanation by @peachpi

- JozelynW

but for the then explain to iris part of the equation i need help on

- JozelynW

##### 1 Attachment

- JozelynW

@pooja195

- JozelynW

@dan815

- JozelynW

@mathmate where did you go?

- JozelynW

@Thesmarterone

- mathmate

I'm here! :)

- JozelynW

for the second part of the question then explain to iris... I need help with that part.

- JozelynW

@mathmate you are gone again

- JozelynW

@prettypink_mega

- anonymous

What was your function in part 1?

- anonymous

They're asking you to compare the features of f(x) from #1 and g(x) from #2.

- JozelynW

f(x)=100(1+0.7)^x

- JozelynW

so how do i do that?

- anonymous

Write a sentence about how the initial populations are different and another sentence about how they are growing at different rates.

- JozelynW

what grade are you in?

- anonymous

none

- JozelynW

finished school

- anonymous

yes

- JozelynW

ok so then please come back because i need help with another question similar to this

- JozelynW

3.)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.

- anonymous

The domain for an exponential function is all real numbers. The range of f(x) is y > 0 because it hasn't been shifted vertically. Plug in 0 for x to get the y-intercept.

- JozelynW

ok

- JozelynW

wait how?

- JozelynW

@peachpi

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