Answer:
The correct option is 1.
Step-by-step explanation:
From the given table it is noticed that the points on the function are [tex](0,\frac{1}{4})\text{ and }(1,1)[/tex]
The general exponential function is defined as
[tex]f(x)=ab^x[/tex]
Where a is initial value and b is growth factor.
The function passing through the point [tex](0,\frac{1}{4})[/tex]. It means the initial value is 1/4.
[tex]a=\frac{1}{4}[/tex]
The function passing through the point (1,1). It means the function must be satisfied by the point (1,1).
[tex]f(1)=ab^1[/tex]
[tex]1=\frac{1}{4}b[/tex]
Multiply both sides by 4.
[tex]4=b[/tex]
The required function is
[tex]f(x)=\frac{1}{4}(4)^x[/tex]
Put x=1,
[tex]f(1)=\frac{1}{4}(4)^1=1[/tex]
Put x=1,
[tex]f(2)=\frac{1}{4}(4)^2=4[/tex]
The ratio of outputs for any two inputs that are one value apart is
[tex]\frac{f(2)}{f(1)}=\frac{4}{1}=4[/tex]
Therefore the ratio of outputs for any two inputs that are one value apart is 4. Option 1 is correct.
