The output value increased by factor 2.
The general form of the exponential function is
f(x)= ab^2
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.
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?