SOLUTION: Find a formula for the exponential function that satisfies g(0)=13 and g(-2)=13/6

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Question 1192789: Find a formula for the exponential function that satisfies g(0)=13 and g(-2)=13/6
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


g%28x%29=ab%5Ex

Knowing g(0), we can find the value of a quickly.

g%280%29=ab%5E0=a%281%29=a=13

So a=13; the equation is g%28x%29=13b%5Ex. Use that in the equation for the other given point to find b.

g%28-2%29=13%28b%5E%28-2%29%29=13%2F6
b%5E%28-2%29=1%2F6
b%5E2=6
b=sqrt%286%29

The exponential function is g%28x%29=13%28%28sqrt%286%29%29%5Ex%29