On a mountain, the temperature decreases by \( 18^{\circ} \mathrm{F} \) for each 5000 -foot increase in elevation. At 7000 feet, the temperature is \( 41^{\circ} \mathrm{F} \). What is the temperature at 22,000 feet? The temperature is Justify your answer.

To determine the temperature at 22,000 feet, we first calculate the elevation change from 7,000 feet to 22,000 feet, which is \( 22,000 - 7,000 = 15,000 \) feet. Since the temperature decreases by \( 18^{\circ} \mathrm{F} \) for every 5,000 feet, the total drop in temperature over 15,000 feet can be calculated as follows: \[ \text{Total decrease} = \left( \frac{15,000 \text{ feet}}{5,000 \text{ feet}} \right) \times 18^{\circ} \mathrm{F} = 3 \times 18^{\circ} \mathrm{F} = 54^{\circ} \mathrm{F}. \] Now, subtract the total decrease from the initial temperature of \( 41^{\circ} \mathrm{F} \): \[ \text{New temperature} = 41^{\circ} \mathrm{F} - 54^{\circ} \mathrm{F} = -13^{\circ} \mathrm{F}. \] The temperature at 22,000 feet is \(-13^{\circ} \mathrm{F}\). This calculation highlights the important concept that altitudes significantly affect temperature by causing it to drop as you ascend. The environmental lapse rate, which describes this decrease, is especially crucial for hiking, mountaineering, or any sort of high-elevation activity. Always pack appropriately for the weather conditions found at higher elevations, even if it feels warm at the base!