To find the rate of change in the mountain goat's elevation as it climbs a cliff, we need to divide the total change in elevation by the time it takes to climb that elevation.
In this case, the elevation change is 50 feet, and the time taken is 22 minutes.
The formula for rate of change is:
\[ \text{Rate of Change} = \frac{\text{Change in Elevation}}{\text{Time}} = \frac{50 \text{ ft}}{22 \text{ min}} \]
Now, we perform the division:
\[ \frac{50}{22} \approx 2.2727 \]
Rounding this to the nearest hundredth, we get:
\[ \approx 2.27 \text{ ft/min} \]
Therefore, the quotient that best represents the rate of change in the goat’s elevation is 2.27 ft/min.