Question: solving for percentage of solved integrand

I have the following integral, which is solved. int(14*t*exp(-t/3),t=0..infinity); It equals 126. I now need to find 90%, of the integral. This is just math and the answer is 113.40. The challenge is I need to prove this using maple. So I need to show how to get the upper limit to 11.67, which yeilds the answer of 113.40(rounded).  I just started pluging in numbers for the upper limit till I got my answer, but clearly, this is now what my instructor wants. I need the process for finding the upper limit. Any help would be appreciated.

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