To determine

To find: Value of C and b for the given function fx=Cbx.

Answer

Answer: fx=213x

Explanation

Graph of fx=Cbx and two points 0,2, 2,2/9 , which means that the value of the given function is 2  at the point x=0  and the value of the function is 2/9  at the point x=2.

 Since given points are (0,2) and (2,2/9), f0=2 and f2=2/9.

Now as f0=2, therefore

 2=Cb0 i.e., C=2.

Also as f2=2/9, therefore

Cb2=29…………. (A)

Put value of C in equation (A), we get b2=19, i.e.,b=±13. Since b is positive, we take b=13. Conclusion: Therefore, fx=213x.