How do you use the model #y=a * b^x# to find the model for the graph when given the two points, (4,256) (3,64)?

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Answer 1 · 2016-08-14T06:37:00

#y=4^x#.

Let us denote, by # C,# the curve #: y=a*b^x#.

We observe that the eqn. of #C# has two unknown consts,, namely,

#a and b#; and as such, to determine them we need two conds.,

given by pts. on #C#.

Given that, pt. #(4,256) in C rArr 256=a*b^4............(1)#, and,

#(3,64) in C rArr 64=a*b^3.................(2)#

To Solve #(1) and (2)#, we divide #(1)# by #(2)#, & get, #b=4#.

Then, by #(2)#, we have, #a=1#.

Therefore, #C# is given by, #y=4^x#.