SOLUTION: Write an exponential function of the form y = ab^x that includes he given points. (1,2) and (4,128)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Write an exponential function of the form y = ab^x that includes he given points. (1,2) and (4,128)      Log On


   

Question 877902: Write an exponential function of the form y = ab^x that includes he given points. (1,2) and (4,128)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Plug in (x,y) = (1,2) and then solve for 'a'


y+=+ab%5Ex


2+=+ab%5E1


2+=+ab


2%2Fb+=+a


a+=+2%2Fb


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Then plug in (x,y) = (4,128). In addition, plug in a+=+2%2Fb. Then solve for b.


y+=+ab%5Ex


128+=+ab%5E4


128+=+%282%2Fb%29%2Ab%5E4


128+=+2b%5E3


128%2F2+=+b%5E3


64+=+b%5E3


b%5E3+=+64


b+=+root%283%2C64%29


b+=+4


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Go back to a+=+2%2Fb and plug in b=4 to find 'a'


a+=+2%2Fb


a+=+2%2F4


a+=+1%2F2


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The equation is y+=+%281%2F2%29%2A%284%29%5Ex