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September 25th, 2017, 05:53 PM   #1
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Question Solving for t

i cant figure out how to solve for t.

550=40t+50e^(-.8t)
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September 25th, 2017, 06:43 PM   #2
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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?
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September 26th, 2017, 07:50 AM   #3
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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.
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September 26th, 2017, 07:56 AM   #4
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Quote:
Originally Posted by fivestar View Post
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.
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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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