To find the rate of change in the goat's elevation, we can use the formula for rate, which is the change in elevation divided by the time taken to change that elevation.
The total change in elevation is 50 feet, and the time taken is 22 minutes.
So the rate of change in the goat's elevation can be calculated as follows:
\[ \text{Rate} = \frac{\text{Change in Elevation}}{\text{Time}} = \frac{50 \text{ feet}}{22 \text{ minutes}} \]
Calculating the quotient:
\[ \text{Rate} = \frac{50}{22} \approx 2.272727272727273 \]
Rounding this to the nearest hundredth:
\[ \text{Rate} \approx 2.27 \text{ feet/minute} \]
Thus, the quotient that best represents the rate of change in the goat’s elevation is 2.27 feet/minute.