This came up in a differential equation, and I wondered if there is an algebraic way to solve this for $t$ without using WolframAlpha. Or is it a case of estimating with a power series?
How do I solve $980 = 98t + 1080e^ \frac{-t}{10}$ for t?
0
$\begingroup$
algebra-precalculus
-
1I'm afraid it will have to be the second option: power series. – 2012-11-18
-
4Some algebraic manipulation (let $z = 98t-980$) and the Lambert W function might do it. – 2012-11-18
-
0@martycohen looks like I'll have to introduce myself to the Lambert W function. – 2012-11-18
-
1Specifically, $t = 10 + 10 W(-54/(49 e))$ where $W$ is any of the branches of the Lambert $W$ function. However, none of the solutions is real. – 2012-11-18