Answer:
The correct option is B.
Step-by-step explanation:
In table A, the function has constant rate of change. For each value of x, the value of y increased by 8.
Since the rate of change of a linear function is constant, therefore table A represents a linear function.
In table B, for each value of x, the value of y is twice of its previous value. In other words we can say that the value of y increases in the same proportion.
[tex]\frac{y_2}{y_1}=\frac{8}{2}=2[/tex]
[tex]\frac{y_3}{y_2}=\frac{16}{8}=2[/tex]
[tex]\frac{y_4}{y_3}=\frac{32}{16}=2[/tex]
[tex]\frac{y_5}{y_4}=\frac{64}{32}=2[/tex]
Therefore it is an exponential function with growth factor 2.
[tex]f(x)=a(2)^x[/tex]
The function passing through the point (1,4).
[tex]4=a(2)^1[/tex]
[tex]2=a[/tex]
The exponential function is
[tex]f(x)=2(2)^x[/tex]
Thus, option B is correct.
In table C, the function has constant rate of change. For each value of x, the value of y increased by 5.
Since the rate of change of a linear function is constant, therefore table C represents a linear function.
In table D, the function has constant rate of change. For each value of x, the value of y increased by 1.
Since the rate of change of a linear function is constant, therefore table D represents a linear function.
