We are asked to write a power function whose graph includes the points (5,9) and (8,34).

Substitute the given x,y pairs into the base model to get two equations with the two unknowns a,b. Solve the resulting simultaneous system:

`9=a*5^b,34=a*8^b`

Solve the first equation for a:

`a=9/(5^b)`

Substitute this expression for a in the second equation:

`34=9/(5^b)8^b`

`34=9(8/5)^b`

`(8/5)^b=34/9`

`b=(ln(34/9))/(ln(8/5))~~2.828`

Substitute this value for b to get a:

`a~~9/(5^2.828)~~0.095`

Thus the model isĀ `y=.0.095x^(2.828)`

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