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

Answer:

Option B is correct

$f(x) = 4^x$

Step-by-step 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, $f(x) = 4^x$