1. **State the problem:** We are given an exponential graph with a point (0,5) and asked to find the exponential function $f(x)$, including the initial value and constant ratio. 2. **Recall the general form of an exponential function:** $$f(x) = a \cdot r^x$$ where $a$ is the initial value (value at $x=0$) and $r$ is the constant ratio (base of the exponential). 3. **Identify the initial value:** From the point $(0,5)$, when $x=0$, $f(0) = a \cdot r^0 = a = 5$. So, the initial value $a = 5$. 4. **Find the constant ratio $r$:** We need another point on the graph to find $r$. The graph shows rapid increase, and from the description, let's use $x=2$ and estimate $f(2)$ from the graph. Assuming $f(2) = 20$ (approximate from the graph). 5. **Use the point $(2,20)$ to find $r$:** $$f(2) = 5 \cdot r^2 = 20$$ Divide both sides by 5: $$\frac{5 \cdot r^2}{\cancel{5}} = \frac{20}{5} \Rightarrow r^2 = 4$$ 6. **Solve for $r$:** $$r = \sqrt{4} = 2$$ 7. **Write the exponential function:** $$f(x) = 5 \cdot 2^x$$ **Final answer:** The exponential function is $f(x) = 5 \cdot 2^x$ with initial value 5 and constant ratio 2.