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Find a formula for the exponential function passing through the points  (-1,2/3) and (1,6) Help much apprieciated can't figure this one out.

 Nov 29, 2019
 #1
avatar+10810 
+1

Find a formula for the exponential function passing through the points  (-1,2/3) and (1,6) Help much apprieciated can't figure this one out.

laugh

 Nov 29, 2019
 #2
avatar+105476 
+2

Here's another approach

 

We have the form

 

y  = ab^x

 

When   x  = -1, y = 2/3

When x  = 1, y  = 6

 

So we have that

 

2/3  = ab^(-1)      (1)

6  =  ab^(1)   ⇒  ab  = 6   ⇒  b = 6/a      (2)

 

Sub (2)   into (1)   and we have that

 

(2/3) =  a  ( 6/a)^(-1)      

 

2/3  =  a ( a /6)      multiply through by 6

 

4  =  a^2      take the positive root

 

2  = a

 

So    b  =   6/2  =  3

 

So....the function is

 

y = 2 (3)^x

 

Here's a praph   :  

 

https://www.desmos.com/calculator/mmoq0kzrez

 

 

 

cool cool cool

 Nov 29, 2019
edited by CPhill  Nov 29, 2019

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