[jknight291]

The concentration of a reacting species is measured and recorded at various time intervals to yield the following data:

time concentration
1 11.2
2 7.73
3 6.23
5 4.80
8 3.80
10 3.36
15 2.76
20 2.37

Engineers analyzing the data have reason to believe that it should be well-described by the model:

C = (alpha*sqrt(1+Beta*t))/t

where C is the species concentration, t is the elapsed time, and alpha and beta are fitted parameters (constants). Find a linearized form for this model, and use linear regression to determine the best-fit values of alpha and beta (give both numerical values and units). Show all intermediate steps and any plots used. Does this model do a good job of describing the data? Do any other simple models describe these data well?

My attempt:

I linearized this model into (ct/alpha)^2 = beta*t +1

From here, though, I'm kind of lost on the linear regression and determining the best-fit models for alpha and beta.

Any help? Thanks.

[sluijten]

I would normally do this type of regression with the Excel built-in solver.
Minimize the sum of errors squared between model and prediction, while varying alpha and beta.
Let me know if you want a more detailed explanation.