`(2,3),(6,12)` Write a power function `y=ax^b` whose graph passes through the given points

We are asked to write a power function whose graph includes the points (2,3) and (6,12).

Substitute the given x,y values into the base equation to get two equations in the two unknowns a,b. Solve the resulting system:

`3=a2^b,12=a6^b`

Solve the first equation for a:

`a=3/(2^b)`

Substitute this expression for a in the second equation:

`12=(3/(2^b))6^b`

`12=3(6/2)^b`

`3^b=4`

`b=(ln(4))/(ln(3))~~1.262`

Use this value to find a:

`a=3/(2^(ln(4)/ln(3)))~~1.251`

Thus the model is `y=1.251x^1.262`

Comments

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