1. **Problem Statement:** We want to find the amount of snow on the ground over time during and after a snowstorm with different rates of snowfall and melting. 2. **Initial Conditions:** At time $t=0$ hours, there are 4 inches of snow on the ground. 3. **First Snowfall:** Snow falls at 2 inches per hour until 4 more inches have fallen. - Time for this snowfall: $$\frac{4 \text{ inches}}{2 \text{ inches/hour}} = 2 \text{ hours}$$ - Snow on ground after this period: $$4 + 4 = 8 \text{ inches}$$ 4. **Storm Stops:** The storm stops for 5 hours, so the snow amount stays constant at 8 inches during this time. 5. **Second Snowfall:** Snow falls again at 3 inches per hour for 4 hours. - Snow added: $$3 \times 4 = 12 \text{ inches}$$ - Snow on ground after this period: $$8 + 12 = 20 \text{ inches}$$ 6. **Melting:** The sun melts snow at 5 inches per hour for 4 hours. - Snow melted: $$5 \times 4 = 20 \text{ inches}$$ - Snow on ground after melting: $$20 - 20 = 0 \text{ inches}$$ 7. **Summary of Snow Amount Over Time:** - From $t=0$ to $t=2$: snow increases from 4 to 8 inches at 2 inches/hour. - From $t=2$ to $t=7$: snow stays constant at 8 inches. - From $t=7$ to $t=11$: snow increases from 8 to 20 inches at 3 inches/hour. - From $t=11$ to $t=15$: snow decreases from 20 to 0 inches at 5 inches/hour. This piecewise linear function describes the snow on the ground over time. **Final answer:** The snow on the ground $y$ as a function of time $t$ (in hours) is: $$ y = \begin{cases} 4 + 2t & 0 \leq t \leq 2 \\ 8 & 2 < t \leq 7 \\ 8 + 3(t - 7) & 7 < t \leq 11 \\ 20 - 5(t - 11) & 11 < t \leq 15 \end{cases} $$ This function can be graphed to show the snow depth over time.