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

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) (Show Source): You can put this solution on YOUR website!
for y = 4, we have
:
1) a(3^n) -23 = 4
:
for y = 220
:
2) a(9^n) -23 = 220
:
Note 3^2 = 9, then equation 2 becomes
:
3) a(3^2n) = 243
:
solve equation 1 for a
:
a = 27/(3^n)
:
substitute for a in equation 3
:
(27/(3^n) * (3^2n) = 243
:
3^n = 243/27
:
3^n = 9
:
n = 2
:
a = 27/9 = 3
:
*************************************
a = 3 and n = 2
:
check the answer
:
3(3^2) -23 = 4
27 -23 = 4
4 = 4
:
3(9^2) -23 = 220
243 -23 = 220
220 = 220
:
our answer checks
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