The Height Of Marie's Seedlings Was Monitored Over A Period Of Four Weeks. The Recorded Heights Were 9 Cm, 18 Cm, K K K Cm, And 72 Cm. Calculate The Height K K K If The Heights Were In Continuous Proportion.

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Introduction

In mathematics, continuous proportion is a concept where the ratio of two quantities remains constant over a period of time. This concept is often used in finance, economics, and other fields to model growth and decay. In this article, we will apply the concept of continuous proportion to calculate the height of Marie's seedlings.

Understanding Continuous Proportion

Continuous proportion is a mathematical concept where the ratio of two quantities remains constant over a period of time. It can be represented by the equation:

$$\frac{a}{b} = \frac{c}{d}$$

where $a$ and $b$ are the initial quantities, and $c$ and $d$ are the final quantities.

Applying Continuous Proportion to Marie's Seedlings

In this problem, we are given the heights of Marie's seedlings over a period of four weeks: 9 cm, 18 cm, $k$ cm, and 72 cm. We are asked to calculate the height $k$ if the heights were in continuous proportion.

To apply the concept of continuous proportion, we can set up the following equation:

$$\frac{9}{18} = \frac{k}{72}$$

Solving for $k$

To solve for $k$, we can cross-multiply the equation:

$$9 \times 72 = 18 \times k$$

$$648 = 18k$$

Now, we can divide both sides of the equation by 18 to solve for $k$:

$$k = \frac{648}{18}$$

$$k = 36$$

Conclusion

In this article, we applied the concept of continuous proportion to calculate the height of Marie's seedlings. We set up an equation using the given heights and solved for $k$. The result is $k = 36$ cm.

Real-World Applications

The concept of continuous proportion has many real-world applications. In finance, it is used to model the growth of investments over time. In economics, it is used to model the demand for a product over time. In biology, it is used to model the growth of populations over time.

Example Problems

Here are a few example problems that demonstrate the concept of continuous proportion:

• A company's sales are increasing at a rate of 10% per year. If the company's sales were $100,000 last year, how much will they be this year?
• A population of bacteria is growing at a rate of 20% per hour. If the population was 1000 bacteria 2 hours ago, how many bacteria will there be now?
• A car's value is decreasing at a rate of 5% per year. If the car's value was $20,000 last year, how much will it be this year?

Tips and Tricks

Here are a few tips and tricks for applying the concept of continuous proportion:

• Make sure to set up the equation correctly by using the correct ratios.
• Use cross-multiplication to solve for the unknown quantity.
• Check your work by plugging the solution back into the original equation.

Conclusion

In conclusion, the concept of continuous proportion is a powerful tool for modeling growth and decay in a variety of fields. By applying this concept, we can solve problems that involve ratios and proportions. We hope that this article has provided a clear and concise explanation of the concept of continuous proportion and how it can be applied to real-world problems.

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Introduction

In mathematics, continuous proportion is a concept where the ratio of two quantities remains constant over a period of time. This concept is often used in finance, economics, and other fields to model growth and decay. In this article, we will apply the concept of continuous proportion to calculate the height of Marie's seedlings.

Understanding Continuous Proportion

Continuous proportion is a mathematical concept where the ratio of two quantities remains constant over a period of time. It can be represented by the equation:

$$\frac{a}{b} = \frac{c}{d}$$

where $a$ and $b$ are the initial quantities, and $c$ and $d$ are the final quantities.

Applying Continuous Proportion to Marie's Seedlings

In this problem, we are given the heights of Marie's seedlings over a period of four weeks: 9 cm, 18 cm, $k$ cm, and 72 cm. We are asked to calculate the height $k$ if the heights were in continuous proportion.

To apply the concept of continuous proportion, we can set up the following equation:

$$\frac{9}{18} = \frac{k}{72}$$

Solving for $k$

To solve for $k$, we can cross-multiply the equation:

$$9 \times 72 = 18 \times k$$

$$648 = 18k$$

Now, we can divide both sides of the equation by 18 to solve for $k$:

$$k = \frac{648}{18}$$

$$k = 36$$

Conclusion

In this article, we applied the concept of continuous proportion to calculate the height of Marie's seedlings. We set up an equation using the given heights and solved for $k$. The result is $k = 36$ cm.

Real-World Applications

The concept of continuous proportion has many real-world applications. In finance, it is used to model the growth of investments over time. In economics, it is used to model the demand for a product over time. In biology, it is used to model the growth of populations over time.

Example Problems

Here are a few example problems that demonstrate the concept of continuous proportion:

• A company's sales are increasing at a rate of 10% per year. If the company's sales were $100,000 last year, how much will they be this year?
• A population of bacteria is growing at a rate of 20% per hour. If the population was 1000 bacteria 2 hours ago, how many bacteria will there be now?
• A car's value is decreasing at a rate of 5% per year. If the car's value was $20,000 last year, how much will it be this year?

Tips and Tricks

Here are a few tips and tricks for applying the concept of continuous proportion:

• Make sure to set up the equation correctly by using the correct ratios.
• Use cross-multiplication to solve for the unknown quantity.
• Check your work by plugging the solution back into the original equation.

Q&A

Q: What is continuous proportion?

A: Continuous proportion is a mathematical concept where the ratio of two quantities remains constant over a period of time.

Q: How is continuous proportion used in real-world applications?

A: Continuous proportion is used in finance, economics, and biology to model growth and decay.

Q: What is the formula for continuous proportion?

A: The formula for continuous proportion is:

$$\frac{a}{b} = \frac{c}{d}$$

where $a$ and $b$ are the initial quantities, and $c$ and $d$ are the final quantities.

Q: How do I solve for the unknown quantity in a continuous proportion problem?

A: To solve for the unknown quantity, you can cross-multiply the equation and then divide both sides by the coefficient of the unknown quantity.

Q: What are some common mistakes to avoid when working with continuous proportion?

A: Some common mistakes to avoid include:

• Not setting up the equation correctly
• Not using the correct ratios
• Not checking your work

Q: Can continuous proportion be used to model negative growth?

A: Yes, continuous proportion can be used to model negative growth. However, the ratio of the quantities will be less than 1.

Q: How do I determine the rate of growth or decay in a continuous proportion problem?

A: To determine the rate of growth or decay, you can use the formula:

$$\frac{a}{b} = \frac{c}{d}$$

where $a$ and $b$ are the initial quantities, and $c$ and $d$ are the final quantities.

Q: Can continuous proportion be used to model exponential growth or decay?

A: Yes, continuous proportion can be used to model exponential growth or decay. However, the ratio of the quantities will be greater than 1.

Conclusion

In conclusion, continuous proportion is a powerful tool for modeling growth and decay in a variety of fields. By understanding the concept of continuous proportion and how to apply it, you can solve problems that involve ratios and proportions. We hope that this article has provided a clear and concise explanation of the concept of continuous proportion and how it can be applied to real-world problems.