Finding coefficients from equation

[bossler]

Hello,
I am stuck on a math problem for one of my engineering courses which seems fairly straight forward, but I have had little success with. The problem reads as follows:
The following data has the form y=ax^b. Estimate the coefficients a+b.
Given data:
Y X
1: (0.0014) (0.5)
2: (0.0251) (2)
3: (0.153) (5)
4: (0.6371) (10)

What I was trying to do was plug in the first set of values and solve the equation for one coefficient in terms of the other. Then I would take the second set of data and plug my answer in, giving me like terms. If someone could explain to me the process of solving this equation I would really appreciate it
Thanks

 

[EnumaElish]

Log y = Log a + b Log x

Use least squares to estimate Log a and b.

 

[HallsofIvy]

The problem does not ask you to FIND the coefficients, it asks you to ESTIMATE them. Putting x and y equal to each pair of given numbers into y= ax^b gives you an equation for a and b. You should only need two equations but you have four and probably can't find a single a and b that will satisfy all four.

From the "extreme" pairs, 0.0014= a (0.5)^b and .6731= a 10^b. Dividing the second by the first eliminates a: .6731/.0014= 0.5^b/10^b which is the same as 480= (1/20)^b= 20^-b. As EnumaElish said, you will need to use logarithms to solve that.

(Thanks to TheoMcCloskey for noting my error. I had started to use the first two points and didn't complete change when I decided to use first and last.)

 

[TheoMcCloskey]

Hall's - I think you better review your response - it needs some corrections.

 

[bossler]

Thank you for the help. I was able to determine the answer both algebraically and on my calculator