SOLUTION: f(x)=a×b^x has the property that f(3)=12 and f(6)=5. Find a and b.

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Question 1148727: f(x)=a×b^x has the property that f(3)=12 and f(6)=5. Find a and b.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Get two equations in a and b using the two given points.

(1) 12+=+a%2Ab%5E3
(2) 5+=+a%2Ab%5E6

Divide the second equation by the first; that eliminates a to give you an equation you can solve for b:

5%2F12+=+b%5E3
b+=+%285%2F12%29%5E%281%2F3%29

Use that in the first equation to find a:

12+=+a%2Ab%5E3+=+a%285%2F12%29
a+=+12%2F%285%2F12%29+=+12%2A%2812%2F5%29+=+144%2F5

ANSWERS:
a = 144/5
b = (5/12)^(1/3)