The graph of an exponential function has a y-intercept of 8 and contains the point (3,64). Find the exponential function that describes the graph.

Given:

Y-intercept of exponential function is 8.

It contains the point (3,64).

To find:

The exponential function that describes the graph.

Solution:

The general form of an exponential function is

     ...(i)

where, a is initial value or y-intercept and b is growth factor.

Since, y-intercept is 8, therefore, a=8.

Put a=8 in (i).

        ...(ii)

It contains the point (3,64). Put x=3 and y=64.

Divide both sides by 8.

On comparing both sides, we get

Put b=2 in (ii).

The functions form of this equation is

Therefore, the required function is .