My Math Forum Solving for t

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 September 25th, 2017, 05:53 PM #1 Member   Joined: Aug 2016 From: illinois Posts: 46 Thanks: 0 Solving for t i cant figure out how to solve for t. 550=40t+50e^(-.8t)
 September 25th, 2017, 06:43 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,202 Thanks: 1157 There is a closed form for the solution of $t$ but it includes a not very commonly seen function known as the Lambert W function. You can read more about it here the solutions are $t = \dfrac{5}{4} \left(W\left(-\frac{1}{e^{11}}\right)+11\right)$ $t = \dfrac{5}{4} \left(W_{-1}\left(-\frac{1}{e^{11}}\right)+11\right)$ The solution involves manipulating the original expression to meet the template of the W function. I leave this to you. Is it possible you are meant to solve it numerically? Thanks from topsquark and Country Boy
 September 26th, 2017, 07:50 AM #3 Member   Joined: Aug 2016 From: illinois Posts: 46 Thanks: 0 im not sure what you mean because we were ever taught that. some websites that i used said to factor out the t but i dont know how to do that with the t on the exponential.
September 26th, 2017, 07:56 AM   #4
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Quote:
 Originally Posted by fivestar im not sure what you mean because we were ever taught that. some websites that i used said to factor out the t but i dont know how to do that with the t on the exponential.
you can't

there's no trick to getting a closed form solution for this expression.

They must intend for you to solve the problem numerically.

September 26th, 2017, 09:09 AM   #5
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Quote:
 550=40t+50e^(-.8t)
$4t+5e^{-0.8t} - 55 = 0$

graph of the rearranged equation shows two solutions ...
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