September 25th, 2017, 04:53 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, 05:43 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,091 Thanks: 1087 
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? 
September 26th, 2017, 06:50 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, 06:56 AM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 2,091 Thanks: 1087  Quote:
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, 08:09 AM  #5  
Math Team Joined: Jul 2011 From: Texas Posts: 2,767 Thanks: 1422  Quote:
graph of the rearranged equation shows two solutions ...  

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