Question 1035044: Find an exponential function of the form f(x) = ab x that passes through the points P.
and Q.
(a) P=(-1,4) and Q=(2,32) (b) P=(-2,32) and Q=(1, 1/2)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find an exponential function of the form f(x) = ab^x that passes through the points P and Q.
(a) P=(-1,4) and Q=(2,32)
4 = ab^-1
32 = ab^2
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Divide the bottom equation by the top and solve for "b"::
8 = b^3
b = 2
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Solve for "a"::
4 = a*2^-1
4 = a/2
a = 8
Equation::
f(x) = 3*2^x
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(b) P=(-2,32) and Q=(1, 1/2)
32 = ab^-2
(1/2) = ab^1
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Divide the bottom equation by the top and solve for "b"::
1/64 = b^3
b = 1/4
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Solve for "a":
32 = a*(1/4)^-2
32 = a*16
a = 2
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Equation:
f(x) = 2*(1/4)^x
OR
f(x) = 2*4^(-x)
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Cheers,
Stan H.
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