Max Z.

asked • 02/13/18

Find the model

Algebraically find the model f(x)=Ca^x so that it satisfies the given conditions.
 
f(2)=9 and f(4)=20.25        f(1)=16 and f(3)=10.24
 
Please tell me how to solve this step by step, so that I can learn it. Having trouble with this. Thanks!

Bobosharif S.

With giving conditions, you can't specify the model. Your model (Ca^x) has two parameters (a, C). To find them you need only two conditions (equations) but you have 4. In pricnicple, having 4 equations should be better, they are more than enough but they are not compatible. So, I suggest to review your question.
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02/13/18

1 Expert Answer

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Mark M. answered • 02/13/18

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I'm assuming that you are asking 2 different questions.
 
The first problem (I think) is:  Find a and C if f(x) = Cax, f(2) = 9 and f(4) = 20.25
 
   f(2) = Ca2 = 9
   f(4) = Ca4 = 20.25
 
Since Ca2 = 9, C = 9/a2
 
So, (9/a2)a4 = 20.25
 
            9a2 = 20.25
 
              a2 = 9/4    Therefore, a = 3/2 
 
                                              C = 9/a2 = 4
 
f(x) = 4(1.5)x
 
Note:  the other problem can be done in a similar manner
 
 
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