Your persistence is commendable. {smile}
As Paddy pointed out, this can be done through LINEST w/o the use of Solver. Irrespective of the method you use, the result will be the same. The below illustrates both approaches.
Suppose your data are in A:B starting with row 2.
First, recognize that now col. B contains the independent variable and A the dependent variable. So, you want to solve for k1 and k2 in the equation A=k1*B^0.5 + k2.
In C2, enter the formula =B2^0.5 Copy C2 as far down C as you have data in B.
Now, in G2:H6 *array enter* the formula =LINEST(A2:A12,C2:C12,TRUE,TRUE)
The solution I got for your data set was 0.003461512*X^0.5+0.025200224
For visual verification, in D2 enter the formula =$G$2*B2^0.5+$H$2. Copy D2 as far down as you have data. Plot A2:B2 making sure A is the y-values and B the x-values. Now, add B & D, again ensuring B are the x-values. You will find the 2 curves are very close together.
The above follows the methodology discussed in the link that Paddy provided.
Here's how to use Solver.
Designate J2 and K2 as the cells that will contain the 2 coefficients. Now, in E2 enter the formula =$J$2*C2+$K$2. In F2 enter the formula =(E2-A2)^2. Copy E2:F2 as far down E as you have data in B.
In first empty cell in F after your data, enter the formula that sums up all the values in F. Using your example for my data set, in F13 I entered =SUM(F2:F12)
Initiate Solver. Set it to minimize F13 by changing J2:K2. Solve the problem. You will get the same results as the LINEST results above.
My saved Solver model:
=MIN($F$13)
=COUNT($J$2:$K$2)
={100,100,0.000001,0.05,FALSE,FALSE,FALSE,1,1,1,0.0001,FALSE}
Ooops. didn't get the data set in there correctly..I amhaving a hard time getting HTML maker working properly. ..The application says it is copying to my clipboard, but then when I press control V to paste it in...there is nothing there. So, here is the data. If I plot the first column vs the second, I get a nice fit. If I plot the second column vs the first, I can't get a good fit, as described above. I'm sorry I'm having such a hard time with this tonight...must be because I should be out having fun instead of beating my head against the wall...
0 0
0.04719 0.068947
0.071965 137.894
0.082583 344.735
0.147469 1172.099
0.18876 2551.039
0.251287 4274.714
0.306735 6136.283
0.359824 9101.004
0.479568 16823.07
0.672458 35783.49
