Answer
$f(x) = 5^x$
Work Step by Step
RECALL:
(1) In the exponential function above, $\dfrac{f(x+1)}{f(x)} = a$
Using the points $(0, 1)$ and $(1, 5)$ and the formula in (1) above,
$\dfrac{5}{1}=a
\\5 = a$
Thus, the tentative equation of the function is $f(x) = C \cdot 5^x$.
To find the value of $C$, use any point on the graph and substitute the x and y values of the point into the tentative equation above. Using the point (1,5) gives:
$f(x) = C \cdot 5^x
\\5 = C \cdot 5^1
\\5 = C \cdot 5
\\\frac{5}{5} = C
\\1 = C$
Thus, the exponential function whose graph is given is $f(x) = 5^x$.