+0

imaginary number wizardry?

0
434
2
+251

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 !

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.

Mar 27, 2018
#2
+111329
+1

10000  =    10000 /  [ 1 + 9e^(-1.13t) ]

Divide both sides by 10000

1  =    1 /  [ 1 + 9e^(-1.13t) ]

1 + 9e^(-1.13t)   =  1

9 e^(-1.13t)  =  0

e^(-1.13t)  =  0

Note that an exponential  can never  = 0

So.....it will  never actually  =  10000

Mar 27, 2018