1. **State the problem:** We are given the function $s = \sqrt{t} + 2$ and need to find the derivative $\frac{ds}{dt}$ at $t = 7$. 2. **Recall the formula:** The derivative of $s$ with respect to $t$ is found by differentiating each term. Recall that $\sqrt{t} = t^{\frac{1}{2}}$ and the derivative of $t^n$ is $nt^{n-1}$. 3. **Differentiate the function:** $$\frac{ds}{dt} = \frac{d}{dt}\left(t^{\frac{1}{2}} + 2\right) = \frac{1}{2}t^{-\frac{1}{2}} + 0 = \frac{1}{2\sqrt{t}}$$ 4. **Evaluate at $t=7$:** $$\frac{ds}{dt}\bigg|_{t=7} = \frac{1}{2\sqrt{7}}$$ 5. **Simplify the answer:** $$\frac{ds}{dt}\bigg|_{t=7} = \frac{1}{2\sqrt{7}}$$ which is the exact value of the derivative at $t=7$. This means the rate of change of $s$ with respect to $t$ at $t=7$ is $\frac{1}{2\sqrt{7}}$.