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
[tex]f(x)=ab^x[/tex] ...(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).
[tex]3=ab^0[/tex]
[tex]3=a(1)[/tex]
[tex]3=a[/tex]
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).
[tex]12=3b^2[/tex]
Divide both sides by 3.
[tex]4=b^2[/tex]
Taking square root on both sides, we get
[tex]\pm \sqrt{4}=b[/tex]
[tex]\pm 2=b[/tex]
Growth factor cannot be negative. So, b=2.
Therefore, the output value increase by factor 2 as each input value increases by 1.
