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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
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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
avatar+103123 
+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

 

 

cool cool cool

 Mar 27, 2018

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