SOLUTION: find exponential equation passes through points(-2,6)and (3,1)

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Question 1193961: find exponential equation passes through points(-2,6)and (3,1)
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Equation or Function?

If you want a form like this, y=ab%5Ex, then the two given points make that system%28ab%5E%28-2%29=6%2Cand%2Cab%5E3=1%29, and you can solve for a and b.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


An exponential function is one of the form y=ab%5Ex.

Given two ordered (x,y) pairs that satisfy the equation, the standard path to the solution starts with plugging each set of x and y values in the general form to get two equations in the parameters a and b. For this example...

6=ab%5E%28-2%29
1=ab%5E3

Then dividing one equation by the other eliminates parameter a, allowing you to solve for b:

1%2F6=b%5E5
b=6%5E%281%2F5%29

Then you can plug this value of b into either original equation to solve for a.

I'll let you do the work. Since the value of b is the 5th root of 6, use a calculator....