Question

Write an equation for the power function, in ax^b form, that passes through the points(2,1) and (5,6).

2nd part: use you power function to predict the value of y when x=9

Answer 1

y=ax^b; plug in (2,1): 1=a(2^b); plug in (5,6): 6=a(5^b).

Divide these two equations to eliminate a: 5^b/2^b=6, which is the same as:

2.5^b=6 and this can be solved using logs: blog(2.5)=log(6), b=1.95545 approx.

Now we can find a=2^-b=0.25784 approx. So y=0.25784x^1.95545.

When x=9, y=18.9375 approx.