\begin{tabular}{l} 14. Mount Everest is growing at a rate of about $$ 1.1 imes 10^{-5} $$ meter per day. \ Express this rate using units of a more appropriate size, and explain why \ the units you chose are more appropriate. \ \hline\end{tabular}

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\begin{tabular}{l} 14. Mount Everest is growing at a rate of about $$ 1.1 	imes 10^{-5} $$ meter per day. \ Express this rate using units of a more appropriate size, and explain why \ the units you chose are more appropriate. \ \hline\end{tabular}

UpStudy AI · Accepted Answer

To express the growth rate of Mount Everest, which is $$ 1.1 \times 10^{-5} $$ meters per day, we can convert this rate into a more appropriate unit, such as centimeters per year.

### Step 1: Convert meters to centimeters
1 meter is equal to 100 centimeters. Therefore, we can convert the growth rate from meters to centimeters:

$$
1.1 \times 10^{-5} \text{ meters/day} = 1.1 \times 10^{-5} \times 100 \text{ cm/day} = 1.1 \times 10^{-3} \text{ cm/day}
$$

### Step 2: Convert days to years
There are approximately 365 days in a year. To find the growth rate in centimeters per year, we multiply the daily rate by the number of days in a year:

$$
1.1 \times 10^{-3} \text{ cm/day} \times 365 \text{ days/year} = 1.1 \times 10^{-3} \times 365 \text{ cm/year}
$$

### Step 3: Calculate the final value
Now, we can perform the multiplication:

$$
1.1 \times 10^{-3} \times 365 = 0.40215 \text{ cm/year}
$$

### Conclusion
Thus, the growth rate of Mount Everest can be expressed as approximately $$ 0.402 $$ cm/year.

### Explanation of Unit Choice
Using centimeters per year is more appropriate than meters per day for the following reasons:
1. **Scale**: The growth of a mountain is a slow process, and expressing it in centimeters per year provides a clearer understanding of the magnitude of the change over a longer time frame.
2. **Context**: In geological terms, changes in elevation are often measured in centimeters or millimeters over years, making this unit more relatable and easier to comprehend for discussions about geological time scales.

In summary, the growth rate of Mount Everest is approximately $$ 0.402 $$ cm/year, which is a more suitable unit for understanding its gradual increase in height.
Mount Everest grows about 0.402 centimeters each year. This unit is better because it shows the slow increase over time in a more understandable way.

\begin{tabular}{l} 14. Mount Everest is growing at a rate of about \( 1.1 \times 10^{-5} \) meter per day. \\ Express this rate using units of a more appropriate size, and explain why \\ the units you chose are more appropriate. \\ \hline\end{tabular}

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