PC: Linear Functions

Question 1

2.1 Example 2: Studies from the early 2010s indicated that teens sent about 60 texts a day, while more recent data indicates much higher messaging rates among all users, particularly considering the various apps with which people can communicate. For each of the following scenarios, find the linear function that describes the relationship between the input value and the output value.
a. The total number of texts a teen sends is considered a function of time in days. The input is the number of days, and output is the total number of texts sent.

Answer 1

f(x) = 60x (p.177)

Question 2

2.1 Example 2: Studies from the early 2010s indicated that teens sent about 60 texts a day, while more recent data indicates much higher messaging rates among all users, particularly considering the various apps with which people can communicate. For each of the following scenarios, find the linear function that describes the relationship between the input value and the output value.
b. A person has a limit of 500 texts per month in their data plan. The input is the number of days, and output is the total number of texts remaining for the month.

Answer 2

f(x) = 500 - 60x (p.177)

Question 3

2.1 Example 2: Studies from the early 2010s indicated that teens sent about 60 texts a day, while more recent data indicates much higher messaging rates among all users, particularly considering the various apps with which people can communicate. For each of the following scenarios, find the linear function that describes the relationship between the input value and the output value.
c. A person has an unlimited number of texts in their data plan for a cost of $50 per month. The input is the number of days, and output is the total cost of texting each month.

Answer 3

f(x) = 50 (p.177)

Question 4

2.1 Example 11: Working as an insurance salesperson, Ilya earns a base salary plus a commission on each new policy. Therefore, Ilya’s weekly income, depends on the number of new policies, he sells during the week. Last week he sold 3 new policies, and earned $760 for the week. The week before, he sold 5 new policies and earned $920. Find an equation for and interpret the meaning of the components of the equation.

Answer 4

I(n) = 80n + 520 (p.187)