Here is the factoids from the original problem:

F(0) = 6

lim(x -> infinity) F(x) = 30

rate of population growth =

where t is a continuous variable and t >= 0

I need to figure out at what t will the population reach 10.

I managed to figure out that A = 46.15, but after that I get lost.

The book says I should be solving for t with the equation

, but I keep coming up with the equation

and I don't know where I am going wrong.

If anyone has some insight for me, that would be super. I've been trying to figure this out for two days now and I need some help.

Thanks.