Solve exponential for t

[KindofSlow]

1180 = 98t + 1080(e^(-0.1t))
Taking the log of both sides doesn't seem to work.
Exponentiating both sides doesn't seem to work.
I think I am either doing something wrong in taking the natural log or not exponentiating correctly or I am missing something else that I think I should know.
Just a little hint would be greatly appreciated.
Thank you

 

[Quaid]

1180 = 98t + 1080(e^(-0.1t))

Hi there:

This particular equation (combination of linear and exponential functions) cannot be solved using algebraic methods at the intermediate-algebra level. (Exact solutions require something known as the LambertW function, I think).

If you subtract 98t from each side, and then graph the resulting left-side and right-side expressions together, you may zoom in on the intersection points, to approximate the solutions to whatever precision you desire.

Cheers :cool:

 

[KindofSlow]

My apologies Jeff.
This is actually one small part of a differential equation problem.
The original problem is: A 50 kg mass is shot from a cannon straight up with an initial velocity of 10m/s off a bridge that is 100 meters above the ground. If air resistance is given by 5v determine the velocity of the mass when it hits the ground.
I didn't post in differential equations because I know and understand all the other steps in the problem and I am a little embarrassed that I am stuck on this part of the problem which seems to be a simple algebra problem.
I have v(t) and my posted equation is s(t) so I'm trying to solve for t when the ball hits the ground and then I can plug in t and solve for v when the ball hits the ground.
Thank you