SOLUTION: Question: Write an exponential function, y=ab^x for a graph that includes points at (1, 12) and (2, 36). I do not understand how to find this. Can you please show me the steps an

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Question: Write an exponential function, y=ab^x for a graph that includes points at (1, 12) and (2, 36). I do not understand how to find this. Can you please show me the steps an      Log On

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Question 191371: Question: Write an exponential function, y=ab^x for a graph that includes points at (1, 12) and (2, 36).
I do not understand how to find this. Can you please show me the steps and answer?
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
y=ab%5Ex Start with the given equation.


12=ab%5E%281%29 Plug in x=1 and y=12. These are the x and y coordinates to the point (1,12)


12=ab Simplify


12%2Fa=b Divide both sides by "a".


b=12%2Fa Rearrange the equation


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y=ab%5Ex Go back to the given equation.


36=ab%5E%282%29 Plug in x=2 and y=36. These are the x and y coordinates to the point (2,36)


36=a%2812%2Fa%29%5E%282%29 Plug in b=12%2Fa


36=a%28144%2Fa%5E2%29 Square 12%2Fa to get 144%2Fa%5E2


36=%28144a%29%2F%28a%5E2%29 Multiply


36=144%2Fa Reduce


36a=144 Multiply both sides by "a".


a=144%2F36 Divide both sides by 36.


a=4 Reduce

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b=12%2Fa Go back to the first isolated equation


b=12%2F4 Plug in a=4


b=3 Reduce


So the exponential equation is y=4%2A3%5Ex