Function { R $}$ Gives The Remaining Amount Of Rice, In Kilograms, As A Function Of The Number Of Weeks Since The Restaurant Owner Bought The Rice.a. Complete The Table:$[ \begin{tabular}{|l|l|} \hline Weeks & Kilograms Of Rice

Introduction

In this article, we will explore the concept of function modeling and its application in real-world scenarios. We will use a specific example to demonstrate how a function can be used to represent a situation and make predictions about the future. The example we will be using is a restaurant owner who bought a certain amount of rice and wants to know how much rice is left after a certain number of weeks.

The Function

The function $f(r)$ gives the remaining amount of rice, in kilograms, as a function of the number of weeks since the restaurant owner bought the rice. This means that if we know the number of weeks, we can use the function to find out how much rice is left.

Completing the Table

To better understand the function, let's complete the table with some values.

Analyzing the Table

From the table, we can see that the amount of rice decreases by 10 kilograms every week. This means that the function $f(r)$ can be represented as a linear function, which is a function of the form $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Finding the Slope

To find the slope, we can use the formula:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line. Let's use the points $(0, 100)$ and $(1, 90)$.

$$m = \frac{90 - 100}{1 - 0} = \frac{-10}{1} = -10$$

Finding the Y-Intercept

To find the y-intercept, we can use the point $(0, 100)$.

$$b = 100$$

Writing the Function

Now that we have the slope and y-intercept, we can write the function as:

$$f(r) = -10r + 100$$

Understanding the Function

The function $f(r) = -10r + 100$ represents the remaining amount of rice, in kilograms, as a function of the number of weeks since the restaurant owner bought the rice. This means that if we know the number of weeks, we can use the function to find out how much rice is left.

Example

Let's say the restaurant owner wants to know how much rice is left after 5 weeks. We can use the function to find the answer.

$$f(5) = -10(5) + 100 = -50 + 100 = 50$$

This means that after 5 weeks, there are 50 kilograms of rice left.

Conclusion

Q&A: Function Modeling and the Remaining Amount of Rice

Q: What is function modeling?

A: Function modeling is a mathematical technique used to represent a situation or a relationship between variables using a function. In the context of the remaining amount of rice, function modeling helps us understand how the amount of rice changes over time.

Q: How does the function $f(r) = -10r + 100$ represent the remaining amount of rice?

A: The function $f(r) = -10r + 100$ represents the remaining amount of rice, in kilograms, as a function of the number of weeks since the restaurant owner bought the rice. The function takes the number of weeks as input and returns the amount of rice left as output.

Q: What is the significance of the slope (-10) in the function?

A: The slope (-10) represents the rate at which the amount of rice decreases per week. In this case, the amount of rice decreases by 10 kilograms every week.

Q: What is the significance of the y-intercept (100) in the function?

A: The y-intercept (100) represents the initial amount of rice when the restaurant owner bought it. In this case, the initial amount of rice was 100 kilograms.

Q: How can we use the function to make predictions about the future?

A: We can use the function to make predictions about the future by plugging in different values for the number of weeks. For example, if we want to know how much rice is left after 10 weeks, we can plug in r = 10 into the function.

Q: What are some real-world applications of function modeling?

A: Function modeling has many real-world applications, including:

• Predicting population growth or decline
• Modeling the spread of diseases
• Understanding the behavior of financial markets
• Optimizing resource allocation
• Predicting the behavior of complex systems

Q: How can we extend the function to model more complex situations?

A: We can extend the function to model more complex situations by adding more variables or using more complex mathematical techniques. For example, we could add a variable to represent the rate at which the amount of rice decreases per week, or use a non-linear function to model the behavior of the system.

Q: What are some common mistakes to avoid when using function modeling?

A: Some common mistakes to avoid when using function modeling include:

• Assuming a linear relationship when the relationship is non-linear
• Failing to account for external factors that can affect the system
• Using an oversimplified model that does not capture the complexity of the system
• Failing to validate the model with real-world data

Conclusion

In this article, we explored the concept of function modeling and its application in real-world scenarios. We used a specific example to demonstrate how a function can be used to represent a situation and make predictions about the future. We also answered some common questions about function modeling and provided some tips for avoiding common mistakes.