Practice Problems
Work through the practice problems. The answers and work follow, then complete the practice quiz.
Practice Problems
1. Suppose that a company purchased a fleet of new cars for its sales force at the cost of $28,000 per year.
The company chooses to depreciate each vehicle using the straight-line method over 7 years.
This means that each car will depreciate by $28,000/7 = $4,000 per year.
A. Build a linear model that expresses book value, V, as a function of its age, x.
B. What is the book value after 3 years?
C. Interpret the slope.
D. Determine when the book value of each car will be $8000.
2. Caroline and Anusha want to track the cost of ice cream at their local ice cream shop, Scoops of Delight, based on how many scoops of ice cream they buy.
Because they are recurring customers, they pay a monthly fee of $2.00, whether or not they buy ice cream that month.
Last month, Anusha paid $4.00 for 3 scoops of ice cream. Two months ago, Caroline paid $7.00 for 4 scoops of ice cream.
What linear equation can we use to describe this relationship?
A. Identify the variables. x = ? y = ?
B. Find the slope.
C. Find the y-intercept.
D. Build a linear model.
E. What is the cost if Caroline wanted just one scoop?
F. Determine the number of scoops if Anusha paid $17.00.
After you check your answers, work on the Practice quiz: Linear Model Quiz.
Answers
Problem 1
A. V(x) represents the value of each car after x years.
V(0) represents the original value of each car, so V(0) = $28,000.
The y-intercept of the linear equation is $28,000.
Each car depreciates by $4,000 per year; the function's slope is -4000.
The linear model represents the book value, V, of each car after x years is V(x) = -4000x + 28000
B. Do this using Desmos
C. V(3) = -4000(3) + 28000 = $16,000
D. The slope (m) is -4000, the average rate of change of the book value is -4000/year. It depreciates -4000 each year.
E. V(x) = 8000 V(x) = -4000x + 28000 = 8000 x = 5 years old
Problem 2
A. x = amount of scoops y = cost of ice cream
B. You have two ordered pairs (4, 7) and (3, 4). m = (7 - 4)/(4 - 3) = 3
C. When the girls don't buy ice cream for a month, they still pay a monthly fee of $2.00. b = 2
D. y = 3x + 2
E. y = 3(1) + 2 = $5.00
F. 17 = 3x + 2, so x = 5 scoops