SOLUTION: Given that y=ax^n-23, and that y=4 when x=3 and y=220 when x=9,find the value of a and of n

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Given that y=ax^n-23, and that y=4 when x=3 and y=220 when x=9,find the value of a and of n      Log On


   

Question 1107734: Given that y=ax^n-23, and that y=4 when x=3 and y=220 when x=9,find the value of a and of n
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
for y = 4, we have
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1) a(3^n) -23 = 4
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for y = 220
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2) a(9^n) -23 = 220
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Note 3^2 = 9, then equation 2 becomes
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3) a(3^2n) = 243
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solve equation 1 for a
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a = 27/(3^n)
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substitute for a in equation 3
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(27/(3^n) * (3^2n) = 243
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3^n = 243/27
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3^n = 9
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n = 2
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a = 27/9 = 3
:
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a = 3 and n = 2
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check the answer
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3(3^2) -23 = 4
27 -23 = 4
4 = 4
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3(9^2) -23 = 220
243 -23 = 220
220 = 220
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our answer checks
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