How do I solve for a? a=b*exp(-at)

[Qacer]

I seem stuck. I thought ln(a) = ln(b) - at, but don't know what to do next.

 

[rcpratt]

Super fail.

 

[Qacer]

But how do I solve for a?

 

[rcpratt]

Oh. I can almost read.

 

[RESmonkey]

Hmph, I am stumped. Wow, didn't think something this elementary could be forgotten. Hold on...

 

[Fenixgoon]

it's a nonlinear equation....

 

[RESmonkey]

Maybe you can't solve for it?

 

[RESmonkey]

it's a nonlinear equation....

this

 

[invidia]

edit

 

[GoSharks]

http://www.wolframalpha.com/input/?i=solve+a+%3D+b*exp(-a+t)+for+a

I have no idea what that means (anymore?) lol.

 

[dullard]

1) Trial and error with guessing.
2) Newton's method (or similar).
3) Use a computer (which will do #2 for you).
4) Graph both sides of the equation and see where they meet.
5) There are plenty more methods, but why bother, since the three above are good enough.

 

[Qacer]

http://www.wolframalpha.com/input/?i=solve+a+=+b*exp(-a+t)+for+a

I have no idea what that means (anymore?) lol.

Ahh.. That's how you use Wolfram Alpha. I tried inputting it earlier, but I put in:

solve for a a=b*exp(-at)

 

[Matthiasa]

First few steps.
a=b*e^(-at)
ln(a)=ln(b)*-at
ln(a)/a=ln(b)*-t
a^(1/a)=b*e^(-t)
Not a nice answer.

 

[Qacer]

1) Trial and error with guessing.
2) Newton's method (or similar).
3) Use a computer (which will do #2 for you).
4) Graph both sides of the equation and see where they meet.
5) There are plenty more methods, but why bother, since the three above are good enough.

I pick 3. ... that in itself may require some time for me to figure out, as well.

 

[dullard]

I pick 3. ... that in itself may require some time for me to figure out, as well.

The most powerful solver that most people have without knowing is Microsoft Excel. In fact, the Excel Solver function is turned off by default (even though it is probably the most powerful part of Excel).

To use it, you need to use the Excel Solver Add-in. In Excel 2007, it is enabled by clicking the round thingy in the top left corner, pressing "Excel options" button, clicking "Add-ins", clicking "go", then checking the "solver Add-in" box. In earlier versions, go to the menu, then look for Add-ins (I forget if it is in the tools menu or not. Enable the "Solver Add-in", you may need the CD (first time only). You only need to do this mess one time.

Then in cell A1, type a guess for "a". In cell B1, type "=b*exp(-A1*t) - A1", where you replace "b" and "t" with the values of "b" and "t". Then use the Excel Solver. (Data menu, then Solver). Set cell B1 equal to value 0 by changing A1. Click "Solve" and you are done. The value you want is now in cell A1.