TUI University Math 101 Nov 2012 Module 5 Professor Dr Karon

Question

TUI Universitymat 101 Nov 2012module 5 Slpprofessor Dr Karonika1 TUI University MAT 101 Nov 2012 Module 5 - SLP Professor: Dr. Karonika 1. The cost of getting new life insurance depends on how old you are, and how old you are depends on what year you were born. Provide an example of a composite function using these variables. 2. The amount of time it takes to get to work depends on how much traffic there is, and the amount of traffic there is depends on what time of day it is. If we call the amount of traffic C and the time of day t, then C is a function of t. If we call the time it takes to get to work W, then W is a function of C. Provide an example of a composite function using these variables. 3. Make up your own example of a composite function. Be sure to explain (1) what your variables are, (2) how they are represented in the function, and (3) which elementary functions are combined to form the composite function. 4. Submit a one to two page paper describing which savings instrument you would prefer and why by the end of the module.

Dr. Jack HW Helper · Accepted Answer

Composite functions are fundamental concepts in mathematics that demonstrate how different functions can be combined to model real-world scenarios. They are formed by applying one function to the results of another, creating a layered or nested function. Below, I explore examples relevant to insurance, traffic, and a personal scenario, illustrating how composite functions can be constructed and interpreted. Example 1: Life Insurance Cost Based on Age Consider a person’s age, which directly influences the cost of purchasing a new life insurance policy. The age, denoted as $A$, depends on the year of birth, represented as $Y_b$. Assume that the current year is fixed at 2012 for this context. The age of an individual can then be expressed as a function of the year of birth: $A = 2012 - Y_b$ This simple linear function shows that if someone was born in 1980, their age in 2012 would be $2012 - 1980 = 32$. Next, suppose the cost of life insurance, $C_i$, depends on age, and this relationship can be modeled through another function: $C_i = f(A)$ Where $f$ could be an increasing function, for example, $f(A) = 50 + 2A$, meaning that as age increases, so does the insurance cost. The composite function combining these is: $C = f(2012 - Y_b)$ This function calculates the insurance cost directly based on the year of birth variable, making it a composite function that links year of birth to insurance cost through age. Example 2: Travel Time Based on Traffic and Traffic Based on Time of Day In the second scenario, the journey duration $W$ depends on the amount of traffic $C$, which in turn depends on the time of day $t$. We can express traffic as a function of time: $C = g(t)$ Where $g$ might be modeled based on typical rush hours, for example: $g(t) = 30 + 20 \sin\left(\frac{\pi t}{12}\right)$ This models traffic fluctuations throughout the day, peaking during certain hours. The travel time $W$ relies on the traffic: $W = h(C)$ Where $h$ could

TUI University Math 101 Nov 2012 Module 5 Professor Dr Karon

TUI Universitymat 101 Nov 2012module 5 Slpprofessor Dr Karonika1

Paper For Above instruction

Example 1: Life Insurance Cost Based on Age

Example 2: Travel Time Based on Traffic and Traffic Based on Time of Day

Example 3: Custom Composite Function

Conclusion

References