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 .

step-by-step explanation:

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~