Question

Function f is an exponential function.

x −4 −2 0 2 4
f(x) 316 34 3 12 48
By what factor does the output value increase as each input value increases by 1?

Answer 1

2

Explanation:

took the test

Answer 2

The output value increased by factor 2.

Explanation:

The general form of the exponential function is

`f(x)=ab^x`

Where, a is initial value and b is growth factor.

From the given table it is noticed that at x=0, the value of f(x) is 3. It means the initial value is 3.

`a=3`

The another value of f(x) is 12 at x=2.

`f(3)=ab^2`

`12=(3)b^2`

`4=b^2`

`b=2`

The required function is

`f(x)=3(2)^x`

Since the growth factor is 2, therefore the output value increased by factor 2.