Question

By what factor does the output value increase as each input value increases by 1​

Answer 1

Given:

The table of values of an exponential function.

To find:

The factor by which the output value increase as each input value increases by 1​.

Solution:

The general exponential growth function is

`f(x)=ab^x` ...(i)

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

From the given table it is clear that the function passes through (0,3). So, put x=0 and f(x)=3 in (i).

`3=ab^0`

`3=a(1)`

`3=a`

From the given table it is clear that the function passes through (2,12). So, put a=3, x=2 and f(x)=12 in (i).

`12=3b^2`

Divide both sides by 3.

`4=b^2`

Taking square root on both sides, we get

`\pm √(4)=b`

`\pm 2=b`

Growth factor cannot be negative. So, b=2.

Therefore, the output value increase by factor 2 as each input value increases by 1​.