To find the rate at which the mountain goat climbs, we can use the formula for rate:
\[ \text{Rate} = \frac{\text{Distance}}{\text{Time}} \]
In this case, the distance the goat climbs is 50 feet, and the time it takes is 22 minutes.
So we calculate the rate:
\[ \text{Rate} = \frac{50 \text{ feet}}{22 \text{ minutes}} \approx 2.27 \text{ feet per minute} \]
If you round this to the nearest hundredth, the result is:
\[ \text{Rate} \approx 2.27 \text{ feet per minute} \]
Therefore, the quotient describing the rate of the goat's elevation is approximately 2.27 feet per minute.