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*16. FORMULATE Suppose that a mountain grows at a rate of 10 inches in 4 years. Express the growth as a unit rate.

Ask by Romero Dunn. in the United States
Mar 11,2025

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The mountain grows at a rate of 2.5 inches per year.

Solution

To express the growth of the mountain as a unit rate, we need to find out how many inches the mountain grows per year. 1. **Identify the known conditions:** - Growth rate: 10 inches - Time period: 4 years 2. **Calculate the unit rate:** - The unit rate can be calculated by dividing the total growth by the total time. - The formula for unit rate \( r \) is given by: \[ r = \frac{\text{Total Growth}}{\text{Total Time}} \] 3. **Substituting the known values:** \[ r = \frac{10 \text{ inches}}{4 \text{ years}} \] 4. **Perform the calculation:** \[ r = 2.5 \text{ inches per year} \] Thus, the growth of the mountain expressed as a unit rate is **2.5 inches per year**.

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Did you know that a unit rate is simply a way to express a quantity divided by one unit of another? In this case, to find the growth rate of the mountain in inches per year, you can divide 10 inches by 4 years. So, the mountain grows at a delightful rate of 2.5 inches per year! Now, when looking at this in a broader context, this concept of growth can relate to real-world phenomena such as climate change and tectonic activity. Mountains are constantly shifting due to geological forces, and understanding their growth rates helps scientists predict changes in landscapes, which can affect ecosystems and human infrastructure. So next time you see a mountain, remember it's not just sitting there—it's growing!

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