How do you find the equation of an exponential function that passes through the points (1,2) and (3,32)?

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Answer 1 · 2018-05-13T01:15:39

#y=4^x/2#

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A general form of an exponential function would be:

#y=ab^x#

Let's plug in the coordinates:

#2=ab^1, :. ab=2, :. a=2/b=2b^(-1)#

#32=a(b)^3#

#32=2b^(-1)b^3#

#32=2b^2#

#16=b^2#

#b=4, :. a=2/b=2/4=1/2#

#y=(1/2)4^x#

#y=4^x/2#