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.Com
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) (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.
\ =\ ab^x)
\ =\ ab^{(0)}\ =\ 9)
But anything raised to the zero power is 1, therefore:
Plugging that value back into the function we have:
\ =\ 9b^x)
Then, given that )
is on the curve, we can say:
}\ =\ 25)
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
\ =\ 9\left(\frac{\sqrt{15}}{3}\right)^x)
John
My calculator said it, I believe it, that settles it
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