Question

What exponential function represents the data in the table?

x f(x)
3 64
4 256
5 1024

ANSWER CHOICES:

f(x) = x4

f(x) = 4x

f(x) = x4 − 17

f(x) = 4x + 17

Answer 1

The answer is C f(x)=x^4-17

Answer 2

Option B is correct

`f(x) = 4^x`

Explanation:

Exponential function is of the form:

`f(x) = ab^x`

where a is the initial amount and b is the growth factor.

Consider any two points from the given tables:

(3, 64) and (4, 256)

Substitute in [1] we have

`64 = ab^3` .....[2]

`256 = ab^4` .....[3]

Divide equation [3] by [2] we get;

`4 = b`

Substitute the value of b in [2] we get;

`64 = a(4)^3`

`64 = a \cdot 64`

Divide both sides by 64 we get;

1 = a

or

a = 1

⇒
`f(x) = 4^x`

therefore, the exponential function represents the data in the table is,
`f(x) = 4^x`