Answer :
The form of the exponential function is
[tex]y=a(b)^x[/tex]Where a is the value of y at x = 0
b is the base of the exponential function
Let us use 2 points from the table to find a and b
∵ At x = 0, y = 4
∵ a is the value of y at x = 0
∴ a = 4
Substitute it in the form of the function
[tex]f(x)=4(b)^x[/tex]Now let us use the point (-1, 4/3)
[tex]\because f(-1)=\frac{4}{3};x=-1\text{and y = }\frac{4}{3}[/tex][tex]\frac{4}{3}=4(b)^{-1}[/tex]Divide both sides by 4
[tex]\begin{gathered} \frac{\frac{4}{3}}{4}=\frac{4b^{-1}}{4} \\ \frac{1}{3}=b^{-1} \end{gathered}[/tex]To change the power of b to +1, reciprocal 1/3
[tex]\begin{gathered} \because\frac{1}{3}=\frac{1}{b} \\ \therefore b=3 \end{gathered}[/tex]The function of the table is
[tex]f(x)=4(3)^x[/tex]The answer is D
