SOLUTION: What is the exponential function (y=ab^x) whose graph passes through the points of (-1, 48) and (2, 6).

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: What is the exponential function (y=ab^x) whose graph passes through the points of (-1, 48) and (2, 6).      Log On


   

Question 730922: What is the exponential function (y=ab^x) whose graph passes through the points of (-1, 48) and (2, 6).
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
What is the exponential function (y=ab^x) whose graph passes through the points of (-1, 48) and (2, 6).
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You have 2 equations to solve for a and b.
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48 = ab^-1
6 = ab^2
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Divide and solve for "b":
8 = b^-3
b = 1/2
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Solve for "a":
6 = a(1/2)^2
6 = a/4
a = 24
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Equation:
y = 24(1/2)^x
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Cheers,
Stan H.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
y=ab%5Ex whose graph passes through the points of
(-1,+48) and (2, 6)
Make a system of equations with the points by substituting them for x and y:
48+=+ab%5E%28-1%29.........1
6+=+ab%5E2.................2
48+=+a%281%2Fb%29.........1
6+=+ab%5E2.................2
take
48+=+a%281%2Fb%29.........1 and solve for a
48b=+a..........substitute in 2
6+=+%2848b%29b%5E2.................2 solve for b
6+=+48b%5E3
6%2F48+=+b%5E3
1%2F8+=+b%5E3
root%283%2C1%2F8%29+=+b
root%283%2C1%29%2Froot%283%2C2%5E3%29+=+b
b=1%2F2
now find a
a+=+48%281%2F2%29
a+=+48%2F2
a=24
The exponential function is y+=+24%281%2F2%29%5Ex.