Question

Which equation represents an exponential function that passes through the point (2,80)

Answer 1

The correct option is D).
`f(x)=5(4)^(x)`

Explanation:

Consider the provided statement:

We need to find the exponential function that passes through the point (2,80),

Now consider the provided option:

The equation
`f(x)=4(x)^(5)` and
`f(x)=5(x)^(4)` are not exponential function. Thus, these two options are wrong.

It is given that the exponential function passes through the point (2,80),

Substitute x = 2 in
`f(x)=4(5)^(x)`.

`f(2)=4(5)^(2)`

`f(2)=4(25)`

`f(2)=100`

Therefore, this function doesn't passes through the point (2,80).

Substitute x = 2 in
`f(x)=5(4)^(x)`.

`f(2)=5(4)^(2)`

`f(2)=5(16)`

`f(2)=80`

Hence, the correct option is D).
`f(x)=5(4)^(x)`.

Answer 2

D

Explanation:

The point (2,80) has the input value x = 2.

Substitute x = 2 into each function.

`f(x) = 5 (4^x)\\f(2) = 5(4^2)\\f(2) = 5 *16\\f(2) = 80`