Answer: D.
Explanation
The exponential function:
[tex]f(x)=a^x[/tex]
Has the form:
Thus, if we evaluate the graph given, we would see that instead of going to the right as the function above, it goes to the left, meaning that whole numbers do not represent our function.
Additionally, we can see that the function represented in the graph has a y-intercept at (0,3):
Meaning that when x = 0, y must be equal to 3.
If we set x = 0 in function C and D we would see that:
[tex]f(0)=5\cdot(\frac{1}{3})^0=5[/tex][tex]f(0)=3\cdot(\frac{1}{5})^0=3[/tex]
Therefore, our function is:
[tex]f(x)=3\cdot(\frac{1}{5})^x[/tex]
