SOLUTION: Please help me get this!! Find the exponential function f(x)=ab^x that goes through (0,9) & (4,25) Please show me the steps, so I can learn!! Thanks so much :-)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help me get this!! Find the exponential function f(x)=ab^x that goes through (0,9) & (4,25) Please show me the steps, so I can learn!! Thanks so much :-)      Log On


   

Question 525050: Please help me get this!!
Find the exponential function f(x)=ab^x that goes through (0,9) & (4,25)
Please show me the steps, so I can learn!!
Thanks so much :-)
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You are panicking for no reason. This is a LOT easier than it looks.

If a point is on a function, then the value of the function must be the coordinate when the coordinate is substituted for .

The first point is so the value of the function must be 9 if the value of is 0.





But anything raised to the zero power is 1, therefore:



Plugging that value back into the function we have:



Then, given that is on the curve, we can say:



A little Algebra Music, Maestro:



Take the positive 4th root of the RHS (the base of an exponetial has to be greater than zero and not equal to 1)



So



John

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