Question

Which exponential function goes through the points (1, 8) and (4, 64)?

a.f(x)=4(2)x
b.f(x)=2(4)x
c.f(x)=4(2)−x
d.f(x)=2(4)−x

Answer 1

The exponential function that goes through (1, 8) and (4, 64) is determined by substituting the points to the given functions:
a. y = f(x) = 4(2)^1 = 8 y = f(x) = 4(2)^4 = 64
Since a already answered the question, the answer is A. f(x)=4(2)x

Answer 2

`f(x)=4(2)^x` is the correct exponential graph.

Explanation:

We have been given the points (1, 8) and (4, 64) and we have to determine from which exponential function these point are passing through.

The y-coordinate in both the points is greater than the y-coordinate. Hence, we must have positive exponent on x. Then only we can get a higher value.

Hence, options c and d can be discarded.

Let us substitute the values for x and y in the first option.

For x = 1

`y=4(2)^1=8`

And for x=4.

`y=4(2)^4=64`

It satisfied the equation.

Therefore,
`f(x)=4(2)^x` is the correct exponential graph.