The functions in option B and option C are exponential function.
What is exponential function?
A mathematical function with the formula f (x) = [tex]a^{x}[/tex] is an exponential function. where an is 'a' constant known as the function's base and 'x' is a variable.
- Step 1: Exponential function for option B.
The data for the values of x and y are given as
x = 0 1 2 3 4
y = 1/3 1 3 9 27
From the data it can be seen that the value of x goes constant change of '1'.
1 - 0 = 1
2 - 1 = 1
3 - 2 = 1
4 - 3 = 1
And the value of y also have the same ratio,
1/(1/3) = 3
3/1 = 3
9/3 = 3
27/3 = 3
- Step 2: Exponential function for option C.
The data for the values of x and y are given as,
x = 0 1 2 3 4
y = 5 5/2 5/4 5/8 5/16
From the data it can be seen that the value of x goes constant change of '1'.
1 - 0 = 1
2 - 1 = 1
3 - 2 = 1
4 - 3 = 1
And the value of y also have the same ratio,
(5/2)/5 = 1/2
(5/4)/(5/2) = 1/2
(5/8)/(5/4) = 1/2
(5/16)/(5/8) = 1/2
Therefore, the functions given in option B and option C are exponential functions.
To know more about the exponential functions, here
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