SOLUTION: Write a power function y = axb whose graph passes through (4, 3) and (8, 7). Round all answers to two decimal places.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Write a power function y = axb whose graph passes through (4, 3) and (8, 7). Round all answers to two decimal places.      Log On


   

Question 259028: Write a power function y = axb whose graph passes through (4, 3) and (8, 7).
Round all answers to two decimal places.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Our power function is
(i) y+=+ax%5Eb
using (4,3), we get
(ii) 3+=+a%2A4%5Eb
using (8,7), we get
(iii) 7+=+a%2A8%5Eb
solving (ii) for a, we get
(iv)a+=+3%2F%284%5Eb%29
substituting (iv) into (iii) we get
(v) 7+=+%283%2F%284%5Eb%29%29%2A8%5Eb
which can be simplified to
(vi) 2.333333+=+2%5Eb
solving for b, we get
b = 1.2224
Now substituting this into (iv), we can get a as
a = .5510
So, our power function becomes
y+=+.55%2Ax%5E%281.22%29