SOLUTION: Write an exponential function y=ab^x whose graph passes through the given points: (2,16), (3,64)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Write an exponential function y=ab^x whose graph passes through the given points: (2,16), (3,64)      Log On


   

Question 144343: Write an exponential function y=ab^x whose graph passes through the given points: (2,16), (3,64)
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
I see several of the same type problme listed. Here is how to solve them. We'll do this one, you do the other using the same process.
Given y=ax%5Eb passes through (2,16) and (3,64)
Then we know
16+=+a2%5Eb and 64=a3%5Eb
4%2A16+=+64
4+%2A+a2%5Eb+=+a3%5Eb+
4%2A2%5Eb+=+3%5Eb+
2%5E2%2A2%5Eb+=+3%5Eb+
2%5E%282%2Bb%29+=+3%5Eb+
%282%2Bb%29%2ALog2+=+b%2ALog3
%282%2Bb%29%2A0.301+=+0.477b
0.602+=+%280.477-0.301%29b
3.42=b

Now use that value of b to find a
16+=+a%2A+2%5E%283.42%29
16%2F10.7+=+a
1.49+=+a
does that work for the other point?
64=1.49%2A3%5E%283.42%29 ???
64+=+1.49+%2A+42.8+
64+=+63.8+ close enough for me. rounding errors
Now use the same idea to do the others. Let me know if you can't get them