# Help With Making Equation from Exponential Growth Graph

label Calculus
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Sep 1st, 2015

We need to find an exponential function that contains the two points (1,9) and (2,27). There are infinitely different ways to do it, because the most generic exponential function is of the form:

y = A*b^(kx) + B, where b is the base, k is the growth rate, A is the initial value and B is a vertical shift. Since the problem just asks for a "possible formula" I will fix B = 0, b=3 and see what k and B need to be so that both points are in the solution:

y = A*3^(kx)

And we need (1,9) and (2,27) to solve it. So we get:

9 = A*3^k

27 =A*3^(2k)

If you divide the second equation by the first equation you get:

3 = 3^(2k)/3^(k), or 3 = 3^k, meaning that k = 1

Then if we plug that back into the first (or second) equation, you get:

9 = A*3, or A = 3

So a possible solution to this exponential function is:

y = 3* 3^(x)

Please let me know if you need any clarification. Always glad to help!
Sep 1st, 2015

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Sep 1st, 2015
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Sep 1st, 2015
Nov 18th, 2017
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