Alan's Bamboo Plant Adds Some Flair To His Apartment. In Four Weeks, Alan Has Trimmed A Total Of 6 2/3 Inches Off The Top Of The Plant. What Is The Rate Of Change In The Plant's Height In Terms Of Inches Per Week? Ignore The Growth Rate Of The Plant.
Calculating the Rate of Change in Alan's Bamboo Plant
Alan's bamboo plant has become a beautiful addition to his apartment, but he's also been diligent about trimming it to maintain its shape. In just four weeks, Alan has trimmed a total of 6 2/3 inches off the top of the plant. But what does this mean in terms of the rate of change in the plant's height? In this article, we'll explore how to calculate the rate of change in the plant's height in inches per week.
To calculate the rate of change in the plant's height, we need to understand what we're trying to find. The rate of change is a measure of how much something changes over a given period of time. In this case, we're interested in the rate of change in the plant's height, which is measured in inches per week.
To calculate the rate of change, we need to divide the total change in the plant's height (6 2/3 inches) by the time over which the change occurred (4 weeks). This will give us the rate of change in inches per week.
Step 1: Convert the Mixed Number to an Improper Fraction
First, we need to convert the mixed number 6 2/3 to an improper fraction. To do this, we multiply the whole number (6) by the denominator (3), and then add the numerator (2). This gives us:
6 × 3 = 18 18 + 2 = 20
So, the improper fraction is 20/3.
Step 2: Divide the Total Change by the Time
Now that we have the total change in the plant's height as an improper fraction (20/3), we can divide it by the time over which the change occurred (4 weeks). To do this, we multiply the numerator (20) by the reciprocal of the denominator (3/4), and then simplify the result.
(20/3) ÷ 4 = (20/3) × (1/4) = (20 × 1) / (3 × 4) = 20/12 = 5/3
Step 3: Simplify the Result
The result of the division is 5/3, which can be simplified to 1 2/3. This means that the rate of change in the plant's height is 1 2/3 inches per week.
In conclusion, by dividing the total change in the plant's height (6 2/3 inches) by the time over which the change occurred (4 weeks), we can calculate the rate of change in the plant's height in inches per week. The result is 1 2/3 inches per week, which means that the plant's height is changing at a rate of 1 2/3 inches per week.
- 1 2/3 inches per week
The final answer is 1 2/3 inches per week.
Frequently Asked Questions (FAQs) About Calculating the Rate of Change in Alan's Bamboo Plant
In our previous article, we explored how to calculate the rate of change in Alan's bamboo plant. We discussed the steps involved in calculating the rate of change, including converting a mixed number to an improper fraction and dividing the total change by the time over which the change occurred. In this article, we'll answer some frequently asked questions (FAQs) about calculating the rate of change in Alan's bamboo plant.
Q: What is the rate of change in the plant's height in inches per week?
A: The rate of change in the plant's height is 1 2/3 inches per week.
Q: How do I convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and then add the numerator. For example, to convert 6 2/3 to an improper fraction, you would multiply 6 by 3 and then add 2, which gives you 20/3.
Q: How do I divide an improper fraction by a whole number?
A: To divide an improper fraction by a whole number, you multiply the numerator by the reciprocal of the denominator. For example, to divide 20/3 by 4, you would multiply 20 by 1/4, which gives you 5/3.
Q: What is the difference between a rate of change and a growth rate?
A: A rate of change is a measure of how much something changes over a given period of time, while a growth rate is a measure of how much something increases over a given period of time. In the case of Alan's bamboo plant, the rate of change is 1 2/3 inches per week, while the growth rate is not specified.
Q: Can I use a calculator to calculate the rate of change?
A: Yes, you can use a calculator to calculate the rate of change. Simply enter the total change in the plant's height (6 2/3 inches) and the time over which the change occurred (4 weeks) into the calculator, and it will give you the rate of change in inches per week.
Q: What if I have a different total change in the plant's height?
A: If you have a different total change in the plant's height, you can simply substitute the new value into the formula and recalculate the rate of change. For example, if the total change in the plant's height is 9 1/2 inches, you would divide 9 1/2 by 4 to get the rate of change.
Q: Can I use this formula to calculate the rate of change in other situations?
A: Yes, you can use this formula to calculate the rate of change in other situations. For example, if you have a total change in a quantity and you know the time over which the change occurred, you can use this formula to calculate the rate of change.
In conclusion, calculating the rate of change in Alan's bamboo plant is a simple process that involves converting a mixed number to an improper fraction and dividing the total change by the time over which the change occurred. By following these steps, you can calculate the rate of change in inches per week and answer frequently asked questions about the process.
- 1 2/3 inches per week
The final answer is 1 2/3 inches per week.