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

         ...(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).

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).

Divide both sides by 3.

Taking square root on both sides, we get

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

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

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