Question

What is the exponential function modeled by the following table? x f(x) 3 8 4 16 5 32 (1 point) f(x) = 2x f(x) = x2 f(x) = x3 f(x) = 3x

Answer 1

the first answer choice, f(x)=2^x

ex: 2^3= 2*2*2=8

Answer 2

First option is correct.

Explanation:

From the given table it is noticed that the exponential function passing through (3,8), (4,16) and (5,32).

Let the exponential function be

`f(x)=ab^x`

The exponential function passing through (3,8).

`8=ab^3` ..... (1)

The exponential function passing through (4,16).

`16=ab^4` ..... (2)

Divide equation 2 by equation 1.

`2=b`

Put this value in equation 1.

`8=a(2)^3`

`8=8a`

`a=1`

The value of a is 1 and the value of b is 2, therefore the function is defined as

`f(x)=2^x`

Therefore first option is correct.