SOLUTION: Write a power Function of the form y=ab^x whose graph passes through the given points: (4,3) (9,4.5)

Question 134605: Write a power Function of the form y=ab^x whose graph passes through the given points: (4,3) (9,4.5)
Found 2 solutions by stanbon, vleith:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Write a power Function of the form y=ab^x whose graph passes through the given points: (4,3) (9,4.5)
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You need to find a and b.
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EQUATIONS:
Substitute to get:
9 = a*b^4.5
3 = a*b^3
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Divide the 2nd equation into the 1st to get:
3 = b^(3/2)
Raise both sides to the (2/3) power to get:
b = 3^(2/3)
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Subsitute to solve for "a":
3 = a^3
3 = a*3^2
a = 3/9 = 1/3
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EQUATION:
y = (1/3)*3^(2x/3)
or
y = (1/3)* (3^(2/3))^x
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Cheers,
Stan H.
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
Use Logs
Given:

Sub in both sets of points. Since Log(a) is the same in both equations, we can set them equal to each other.

Now solve for a

Function is:

Verify the function by plugging in the given points
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