Question

solve for t, t=(10x+1)e^(t)

Answer 1

Obviously we can solve for x fairly readily:
\[t=(10x+1)e^t\]
\[te^{-t}=(10x+1)\]
\[\frac{te^{-t}-1}{10}=x\]
It isn't quite as meaningful to solve for t when the same value of x (-.08 for instance) corresponds to multiple values for t. We would need to split into different functions. Let's find a critical point where dx/dt = 0 and snap the curve there.

Answer 2

I finally got it, its a transcendental equation where you have to approx the e^t term, just figured it out

Answer 3

I'm looking at the Lambert W-function. Learn something new...