Solve for t: y₀e^-kt = y₀ / 2 y₀ > 0, k >0

 

I have no idea how to approach this problem. I don't even know what category this falls under so I'm having trouble googling info this type of problem.

I don't see your problem. What if [math]y_0[/math] was called c? Do you think that would make a difference? Does "solve [math] ce^{-kt} = \frac c2[/math] for t" look easier to you? If so, then solve that. If not, then there must be something special about the [math]y_0[/math] that you did not tell us. The way the problem is stated it is just some non-zero constant.

My main problem is I don't know why they give me the info "y0 > 0, k >0". I can isolate t and get t = ln0.5 / -k but I'm assuming they give me that extra info so I can figure out what k is in order to fully solve for t.

k has to be nonzero so that your equation there won't have division by 0. If y₀ were 0, the equation would be ludicrously simple, since it'd just be 0 = 0. The constraints are just there to make it all work.

Ah right. Thanks.