1. **State the problem:** We need to write an exponential function for the graph labeled 10, which passes through (0,1), is increasing, and levels off near 4 as $x$ increases. 2. **Identify the type of function:** Since the graph levels off near 4, it suggests a horizontal asymptote at $y=4$. This is typical of a transformed exponential function of the form: $$y = A(1 - Be^{-kx}) + C$$ where $C$ is the horizontal asymptote. 3. **Use the given points and behavior:** The graph passes through (0,1), so: $$y(0) = A(1 - B e^{-k \cdot 0}) + C = A(1 - B) + C = 1$$ The horizontal asymptote is $y = 4$, so $C = 4$. 4. **Substitute $C=4$ into the equation:** $$A(1 - B) + 4 = 1$$ Simplify: $$A(1 - B) = 1 - 4 = -3$$ 5. **Since the function is increasing and levels off at 4, a common form is:** $$y = 4 - 3 e^{-kx}$$ Check at $x=0$: $$y(0) = 4 - 3 e^{0} = 4 - 3 = 1$$ which matches the point (0,1). 6. **Confirm the behavior:** As $x \to \infty$, $e^{-kx} \to 0$, so $y \to 4$, the horizontal asymptote. 7. **Final function:** $$\boxed{y = 4 - 3 e^{-kx}}$$ where $k > 0$ controls the rate of increase. Since no other points are given to find $k$, this is the general form of the function.