Question

A mountain goat is climbing to the top of a large cliff. The cliff is 50 feet higher than its starting point. If it takes the goat 22 minutes to climb this cliff, interpret the quotient to describe the rate of change in the goat’s elevation. Give your answer to the nearest hundredth.(1 point)
The quotient that best represents the rate of change in the goat’s elevation is answer goes here feet/minute.

Answer 1

To find the rate of change in the goat's elevation, we need to calculate the elevation change per unit of time.

The goat climbs a cliff that is 50 feet high in 22 minutes. To find the rate of change in elevation, we will divide the total elevation gained by the total time taken:

\[
\text{Rate of change} = \frac{\text{Total elevation gain}}{\text{Total time}} = \frac{50 \text{ feet}}{22 \text{ minutes}}.
\]

Now, we can calculate this quotient:

\[
\text{Rate of change} = \frac{50}{22} \approx 2.27272727.
\]

To round this to the nearest hundredth, we look at the third decimal place (which is 2 in this case). Since it is less than 5, we leave the second decimal place as it is.

Thus, rounding gives us:

\[
\text{Rate of change} \approx 2.27 \text{ feet/minute}.
\]

So, the final answer is:

**2.27 feet/minute.**