1. **State the problem:** We need to find a linear model for the altitude $A$ (in feet) of a jet $t$ minutes after takeoff, given it passed 12,000 feet at 8 minutes and climbs at 1,250 feet per minute. 2. **Formula and explanation:** A linear model has the form $$A = mt + b$$ where $m$ is the rate of change (slope) and $b$ is the initial altitude at $t=0$. 3. **Identify known values:** The rate of climb $m = 1250$ ft/min. At $t=8$, $A=12000$ ft. 4. **Find $b$ (initial altitude):** Substitute known values into the model: $$12000 = 1250 \times 8 + b$$ $$12000 = 10000 + b$$ $$b = 12000 - 10000 = 2000$$ 5. **Write the linear model:** $$A = 1250t + 2000$$ 6. **Predict altitude at $t=28$ minutes:** $$A = 1250 \times 28 + 2000 = 35000 + 2000 = 37000$$ **Final answer:** The linear model is $$A = 1250t + 2000$$ and the predicted altitude at 28 minutes is 37000 feet.