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.

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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.

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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@pooja195 please help me
\[g(x)=200(1.03)^{2x}=200(1.03^2)^x\] Growth rate formula \[g(x)=A(1+r)^x\] A = initial amount, r = growth rate
the answer is g(x)=200(1.0609)^x. I need help with the second part of the question @peachpi

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@peachpi Then explain to Iris...... how do i do that part?
do you know
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
but for the then explain to iris part of the equation i need help on
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@mathmate where did you go?
I'm here! :)
for the second part of the question then explain to iris... I need help with that part.
@mathmate you are gone again
What was your function in part 1?
They're asking you to compare the features of f(x) from #1 and g(x) from #2.
f(x)=100(1+0.7)^x
so how do i do that?
Write a sentence about how the initial populations are different and another sentence about how they are growing at different rates.
what grade are you in?
none
finished school
yes
ok so then please come back because i need help with another question similar to this
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.
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.
ok
wait how?

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