SOLUTION: A function that can be written in the form y = ax^b is said to be a power function. Some data sets can best be modeled by a power function. On a TI-83/84 calculator, the PwrReg

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Question 1006256: A function that can be written in the form
y = ax^b
is said to be a power function. Some data sets can best be modeled by a power function. On a TI-83/84 calculator, the PwrReg instruction is used to produce a power regression function for a set of data. Find the power regression function for the following data. (Round your numerical values to five decimal places.)
x 1 2 3 4 5 6
y 2.4 5.4 9.7 14.4 19.8 26.0
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+ax%5Eb

x%09|1%09|2%09|3%09|4%09|5%09|6
y%09|2.4%09|5.4%09|9.7%09|14.4%09|19.8%09|26.0

use given table to set the system of two equations and find a and b
y+=+ax%5Eb..........if x=1 and y=2.4
2.4+=+a%281%29%5Eb............eq.1
y+=+ax%5Eb..........if x=2 and y=5.4
5.4+=+a%282%29%5Eb............eq.2
solve the system:
2.4+=+a%281%29%5Eb............eq.1
5.4+=+a%282%29%5Eb............eq.2
--------------------------------------take a logarithm of both sides
log%282.4%29+=+log%28a%281%29%5Eb%29............eq.1
log%285.4%29+=+log%28a%282%29%5Eb%29............eq.2
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log%282+4%2F10%29+=+log%28%28a%29%29%2Blog%28%281%29%5Eb%29%29............eq.1
log%285+4%2F10%29+=+log%28%28a%29%29%2Blog%28%282%29%5Eb%29%29............eq.2
------------------------------------------------
log%2824%2F10%29+=+log%28%28a%29%29%2Bb%2Alog%28%281%29%29............eq.1
log%2854%2F10%29+=+log%28%28a%29%29%2Bb%2Alog%28%282%29%29............eq.2
------------------------------------------------
log%2824%2F10%29+=+log%28%28a%29%29%2Bb%2Alog%28%281%29%29............eq.1......since b%2Alog%28%281%29%29=0 we have
log%2824%2F10%29+=+log%28%28a%29%29...........if log same then
a=24%2F10
find b
log%2854%2F10%29+=+log%28%28a%29%29%2Bblog%28%282%29%29............eq.2
log%2854%2F10%29+=+log%28%2824%2F10%29%29%2Bb%2Alog%28%282%29%29
log%2854%29-log%2810%29+-%28+log%2824%29-log%2810%29%29=b%2Alog%28%282%29%29

log%2854%29-+log%2824%29=b%2Alog%28%282%29%29
log%2854%2F24%29%2Flog%28%282%29%29=b
log%289%2F4%29%2Flog%28%282%29%29=b
b=log%283%5E2%2F4%29%2Flog%28%282%29%29
b=%28log%283%5E2%29-log%284%29%29%2Flog%28%282%29%29
b=%282log%283%29-log%284%29%29%2Flog%28%282%29%29


your function is:
it doesn't fit; next to y=ax%5Eb=%2824%2F10%29 should be x to the power of %282log%283%29-log%284%29%29%2Flog%28%282%29%29%29