SOLUTION: I need help with this question: find an exponential function going through the points (3,54) and (4,162). Then write your function as a base of e. I do not know how to find the fun

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Question 716002: I need help with this question: find an exponential function going through the points (3,54) and (4,162). Then write your function as a base of e. I do not know how to find the function, or how to write it with base e.
I attempted this problem by solving for a=33.72 and b=1.17 , but I do not know if that is right.
I came to have the function y=33.72 (1.17)^x and the base of e function to be f(t)=33.72e^1.17t
Answer by josgarithmetic(39625) (Show Source):
You can put this solution on YOUR website!
The key to solving this is to try to factor each of the y coordinates. See how they relate to the x coordinates. To be thorough, find the complete prime factorization of y coordinate of each point.

, and

You see a base of 3. The 2 is working as a coefficient. Now recheck the points using the complete factorizations of y.
(3,) and (4,).
Each point is found according to a formula, (, ).

That should be all you need to continue and finish solving the problem.
(Obvious now is the function is ).