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Converting units is a fundamental part of solving many mathematical problems. In this exercise, we convert the height of the trees from feet to inches. To do this, we use the knowledge that 1 foot equals 12 inches.
For example, for the tallest tree, we multiply 367.5 feet by 12 to find the tree's height in inches.
This calculation looks like this: \( 367.5 \text{ feet} \times 12 \text{ inches/foot} = 4,410 \text{ inches} \).
Converting units ensures all measurements are in the same form, making further calculations easier to handle.

Percentage calculations help compare different quantities relative to each other. Here, we find what percentage the height of the second tree is of the tallest tree. To convert a value into a percentage, we divide the part by the whole and then multiply by 100.
For example, we have the height of the nearby redwood (363.4 feet) and the height of the tallest tree (367.5 feet).
We calculate the percentage by using the formula: \( \frac{363.4 \text{ feet}}{367.5 \text{ feet}} \times 100 = 98.88\% \).
This tells us that the second tree's height is approximately 98.88% of the tallest tree's height.

A growth rate indicates how much something increases over a specific period. In the exercise, we calculate the average growth rate of the tallest tree in inches per year. This requires knowing the total growth and the number of years over which this growth occurred.
We first converted the tree's height from feet to inches (4,410 inches). We then divided this by the tree’s estimated age range (600 to 800 years).
So, the calculation for 600 years looks like this: \( \frac{4,410 \text{ inches}}{600 \text{ years}} = 7.35 \text{ inches/year} \), and for 800 years: \( \frac{4,410 \text{ inches}}{800 \text{ years}} = 5.5125 \text{ inches/year} \).
This means the tree grew approximately between 5.51 and 7.35 inches per year on average.

Mathematical problem solving involves applying various techniques and concepts to find solutions. In this exercise, we used unit conversion, percentage calculations, and average growth rate formulas.
Breaking down the problem step-by-step keeps things manageable:

• Convert the height of the tree into the same units to maintain consistency.
• Use division to find average values, such as the growth rate over time.
• Apply percentage formulas to compare different values.

Mastering these steps and knowing when to use each technique is key to solving mathematical problems effectively.