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Find the exponential function that contains the points (1,27) and (5,2187). Please show steps to the solution.

 Dec 18, 2019
edited by Guest  Dec 18, 2019
 #1
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We have the form

 

y = ab^x

 

And we know that

 

27 = ab^1   ⇒  27 = ab   ⇒  27/b  =  a     (1)

2187  = ab^5        (2)

 

Sub  (1)  into (2)  for  a

 

2187  =  (27/b) * b^5     divide both sides by 27  and simplify

 

2187/ 27  =  b^4

 

81  =  b^4       take the positive 4th root

 

81^(1/4) =  b   =   3

 

And    27/b = a =    27/3   =  9

 

So....the function  is

 

y =  9 * 3^x

 

 

cool cool cool

 Dec 18, 2019

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