Initial Post Instructions In The Real World Functions Are Ma

Initial Post Instructionsin The Real World Functions Are Mathematical

In the real world, functions are mathematical representations of input-output situations. A vending machine is one such example. The input is the money combined with the selected button. The output is the product. Here is another example: The formula for converting a temperature from Fahrenheit to Celsius is a function expressed as: C = (5/9)*(F - 32), where F is the Fahrenheit temperature and C is the Celsius temperature.

If it is 77 degrees Fahrenheit in Phoenix Arizona, then what is the equivalent temperature on the Celsius thermometer? Our input is 77. C = (5/9)() C = (5/9)(45) C = 25 The equivalent temperature is 25 degrees Celsius. To complete the Discussion activity, please do the following: Choose your own function or choose from the list below and then provide a unique example of a function and evaluate the function for a specific input (like the example above). Arm length is a function of height. The circumference of a circle is a function of diameter. The height of a tree is a function of its age. The length of person's shadow on the ground is a function of his or her height. Weekly salary is a function of the hourly pay rate and the number of hours worked. Compound interest is a function of initial investment, interest rate, and time. Supply and demand: As price goes up, demand goes down.

Paper For Above instruction

The concept of functions as mathematical representations of real-world input-output relationships is fundamental in understanding various phenomena in daily life and economic activities. By examining different examples, we can appreciate how functions help model relationships, make predictions, and inform decision-making. In this paper, I will select and evaluate a specific function from the provided list, demonstrating how input variables are transformed into outputs through the application of mathematical formulas.

For this exercise, I have chosen the function representing the relationship between weekly salary, hourly pay rate, and hours worked. Specifically, weekly salary (W) is modeled as a function of hourly pay rate (h) and the number of hours worked (H). Mathematically, this can be expressed as:

W = h × H

This simple yet powerful function embodies the proportional relationship between hourly earnings and total weekly income, assuming no overtime or taxes for simplicity. To evaluate this function, I will assign specific values to the variables: suppose an individual earns $20 per hour and works 40 hours in a week.

Using the formula:

W = 20 × 40 = $800

This calculation reveals that the weekly salary for an individual earning $20 per hour and working 40 hours is $800. This straightforward example highlights how the function effectively models real-world income scenarios, allowing individuals and businesses to project earnings based on hourly compensation and hours worked.

Additionally, this basic model can be extended to incorporate overtime pay, taxes, and other factors, making it more comprehensive. For example, if overtime is paid at 1.5 times the regular rate for hours exceeding 40, the function would modify accordingly:

W = (h × 40) + (1.5 × h × (H - 40)), for H > 40

In conclusion, functions serve as essential tools for translating real-world variables into quantifiable outputs. The example of calculating weekly salary demonstrates how a simple function can be used to interpret everyday economic data, inform financial planning, and prepare for different scenarios. Understanding these relationships empowers individuals and organizations to make informed decisions based on mathematical models that mirror reality.

References

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  • Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2019). Quantitative Methods for Business. Cengage Learning.

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