1. **Stating the problem:** We need to write the domain and function of $b(x)$ based on the graph description. 2. **Understanding the graph:** The function $b(x)$ starts near zero cost when $x=0$ units and rises steeply, then levels off around 320 at about 600 units. 3. **Domain:** Since the graph shows $b(x)$ from 0 units to about 600 units, the domain is $0 \leq x \leq 600$. 4. **Function form:** The curve starts steep and then levels off, which suggests a function that increases quickly and approaches a horizontal asymptote. A common model is an exponential decay approaching a limit or a logistic-type function. Here, we can model $b(x)$ as a function approaching 320 as $x$ approaches 600. 5. **Example function:** One possible function is $$b(x) = 320\left(1 - e^{-kx}\right)$$ where $k$ is a positive constant controlling the steepness. 6. **Explanation:** At $x=0$, $b(0) = 320(1 - e^{0}) = 320(1 - 1) = 0$, matching the graph start. As $x$ increases, $e^{-kx}$ decreases, so $b(x)$ approaches 320. 7. **Summary:** - Domain: $0 \leq x \leq 600$ - Function: $b(x) = 320\left(1 - e^{-kx}\right)$ for some $k > 0$ This matches the graph behavior described.