+0  
 
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avatar+483 

Let F(x)=12/3+ae^kx with f(0)=2 and f(1)=1/2

 

 

The value of a is ____???

 

The value of k is ____????

 

F(3)_____????

 Mar 25, 2020
 #1
avatar+23566 
+3

*** deleted ***

 

I solved    12/3    + aekx

 

When the question SHOULD have read    12 / ( 3+aekx)           Use the correct syntax people !  It IS VERY IMPORTANT !!!!

 

See Chris' answer below

 Mar 25, 2020
edited by ElectricPavlov  Mar 25, 2020
edited by ElectricPavlov  Mar 26, 2020
 #2
avatar+1956 
+2

Nice, EP!

CalTheGreat  Mar 25, 2020
 #3
avatar+111321 
+1

I think this is supposed to be a logistics  growth/decay  equation.....we  have   that

 

                           12

f(x)   =           _________ 

                        a + e^(kx)

 

We know that   f(0)  = 2      this makes   e^(kx)   =  e^(k*0)  =  1

 

So

 

                  12

  2 =        _____

                 a + 1

 

Means that   a  =   5

 

And   f(1)  =  1/2      ....so.......

 

 

                            12

1/2    =            _________           rearrange as  

                         5 + e^(k)

 

 

5 + e^(k)  =  12   /   (1/2)

 

5  +  e^k   =   24        subtract    5 from both sides

 

e^k =    19         

 

This   implies  that     

 

Ln e^k  = Ln 19

 

k * Ln e   =   Ln 19

 

k * (1)  = Ln 19

 

k = Ln 19

 

 

f(3)   =           12   /  [ 5  + e^(3 * Ln 19) ]   =      1  / 572

 

Here's the graph : https://www.desmos.com/calculator/9lngaoxfod

 

 

cool cool cool

 Mar 26, 2020

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