I have the function:

\(P(t)=\frac{10000}{1+9e^{-1.13t}}\)

I'm trying to solve for the time it takes to reach P = 10,000

that is,

\(\textrm{Solve for t}\\ 10000=\frac{10000}{1+9e^{-1.13t}}\)

after graphing I can see that the answer is t = 10, However I wish to solve this explicitly / analytically.

I get to the point of:

\(0 = e^{-1.13t}\)

and then I'm lost from there.

your help is greatly appreciated !

vest4R
Mar 27, 2018

#1**0 **

The only way you can get P(t) =10,000 is to have your denominator = 1 exactly!. Even if t =1,000,000

then you would have: e^(-1,130,000), which of course means: 1 / (e^1,130,000), which is very close to zero, but NOT exactly zero!. In fact e^(-1,130,000) =1.719686672 E-490,753.

Guest Mar 27, 2018