The value of exponential function, which completes the table for variable x at 1/3 is 3. The option B is correct.
Exponential function is the function in which the function growth or decay with the power of the independent variable.
The curve of the exponential function depends on the value of its variable.
The exponential function with dependent variable y and independent variable x can be written as,
[tex]y=a^x[/tex]
Here, [tex]x[/tex] is the variable in the power of a number.
Given information-
The given exponential function in the problem is,
[tex]f(x)=8^x+1[/tex]
The value of function at the value of variable x as 1/3 has to be find to complete the table. Put 1/3 in the above equation on the place of x as,
[tex]f(x)=8^{\frac{1}{3}}+1[/tex]
The number 8 can be written as the [tex]2^3[/tex]. Thus,
[tex]f(x)=(2^3)^{\frac{1}{3}}+1\\f(x)=(2)^{\dfrac{3\times1}{3}}+1\\f(x)=(2)^1+1\\f(x)=2+1\\f(x)=3[/tex]
Thus the value of exponential function, which completes the table for variable x at 1/3 is 3. The option B is correct.
Learn more about the exponential function here;
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