Question 549870: How do I make the equation y=ab^x with two points, (5,4) and (7,9)?
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How do I make the equation y=ab^x with two points,
(5,4) and (7,9)?
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Solve for a and b:
Using (7,9) you get 9 = ab^7
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Using (5,4) you get 4 = ab^5
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Divide the lower into the higher equation:
(9/4) = b^2
b = 3/2
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Substitute for "b" and solve for "a":
9 = ab^7
9 = a(3/2)^7
---
a = 9/(3/2)^7 = 0.5267
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Equation:
y = (0.5267)(3/2)^x
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Cheers,
Stan H.
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Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! How do I make the equation y=ab^x with two points, (5,4) and (7,9)?
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4 = a*b^5
9 = a*b^7
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log(4) = log(a) + 5log(b)
log(9) = log(a) + 7log(b)
--------------------------- Subtract
log(4/9) = -2log(b) = 1/log(b^2)
b^2 = 9/4
b = 3/2
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4 = a*b^5 = a*(3/2)^5
a = 4*(2/3)^5
a = 128/243
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y = (128/243)*(3/2)^x
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