Question

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.

Answer 1

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

$y=ab^x$      ...(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).

$y=8b^x$         ...(ii)

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

$64=8b^3$

Divide both sides by 8.

$\dfrac{64}{8}=b^3$

$8=b^3$

$2^3=b^3$

On comparing both sides, we get

$b=2$

Put b=2 in (ii).

$y=8(2)^x$

The functions form of this equation is

$f(x)=8(2)^x$

Therefore, the required function is $f(x)=8(2)^x$.

Answer 2

Answer: Do you have a picture

Step-by-step explanation: