Interpreting Parameters of Linear Functions (Grade 9)

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Interpreting Parameters of Linear Functions

1. 
A taxi charges an initial flat fee, plus a per mile rate. If the function [math]T(m) = 2.5 + 0.75m[/math] represents the total cost of a trip, where [math]T[/math] is measured in dollars and [math]m[/math] in miles, what is the per mile rate the taxi charges?
  1. $2.50 per mile
  2. $0.75 per mile
  3. $3.25 per mile
  4. This can't be determined without knowing the exact number of miles the taxi has driven for a specific fare.
2. 
Anne is a mechanic at a car store. She earns a regular monthly salary, and then an extra hourly wage if she has worked overtime that month. If the function [math]P(t) = 2250 + 32t[/math] represents how much Anne earns in a month in dollars, given how much overtime she has worked in hours, what does the term 2,250 represent?
  1. Her hourly wage.
  2. Her total income for the month.
  3. Her monthly base salary.
  4. The number of overtime hours she has worked.
3. 
A bucket, with some water already in it, is left out in the rain. As it rains, the volume of water in the bucket increases. If the function [math]W(t) = 2.8 + 0.1t[/math] represents this situation, where [math]W[/math] is the volume of water in liters and [math]t[/math] is the time the bucket has been left outside (measured in hours), what does the coefficient 0.1 represent?
  1. The rate at which the water level is increasing.
  2. The current water level.
  3. The amount of time that has passed.
  4. The extra amount of water the has accumulated.
4. 
Shawn put some money into an account that earns simple interest according to the function [math]A(t) = 1000*(1+0.015t)[/math], where [math]A[/math] is the amount of money in the account after [math]t[/math] years. What does the value 1,000 represent?
  1. The total value of money in the account after [math]t[/math] years.
  2. The interest earned after [math]t[/math] years.
  3. The initial investment.
  4. The interest rate, as a percent.
5. 
Clinton recently started working at a small library and is responsible for returned books. Each day when he begins, there are some books already waiting by the return slot in the door. As the day progresses, more people return books. Clinton first thought that the function [math]B(t) = 15h + 4[/math] models the number of books returned during a day, where [math]B[/math] is the total number of books returned on a single day, and [math]h[/math] is the number of hours since the library opened. After a few more days, Clinton realizes he was wrong, and that books are returned more frequently during the day than he had originally estimated. Which of the following functions could be a possible alternative?
  1. [math]B(h) = 16h + 3[/math]
  2. [math]B(h) = 15h + 4 + 5t[/math]
  3. [math]B(h) = 15h + 5[/math]
  4. [math]B(h) = 20h + 4[/math]
6. 
Shea owns a bakery, and primarily sells bread. He has found that he can approximately model his expenses each month with the function [math]E(b) = 7b + 700[/math], where [math]E[/math] is Shea's total monthly expenses in dollars, and [math]b[/math] is the number of loaves of bread he sells each month. Which of the following statements about his expenses is correct? There may be more than one correct answer.
  1. His monthly expenses are $707.
  2. It costs about $7 to make each loaf of bread.
  3. Shea has about $700 in fixed expenses each month.
  4. Shea will only break even (make more money than he has to spend in expenses) if he sells at least 100 loaves of bread.
7. 
Kelly runs an arcade. She charges an entrance fee, and then each game costs a small amount each time someone wants to play it. If the function [math]M(p) = 5 + 0.5p[/math] represents how much money someone would have to pay in dollars for playing [math]p[/math] games, what is the entrance cost?
  1. $5
  2. $0.50
  3. $5.50
  4. It depends on the number of games that person played.
8. 
A car is traveling at 15 mph, and then begins to accelerate. The function [math]v(t) = 15 + 9t[/math] models this, where [math]v[/math] measures the speed of the car in miles per hour, and [math]t[/math] is the time elapsed in seconds since the car started accelerating. How fast is the car accelerating?
  1. 15 mph/s
  2. 9 mph/s
  3. 24 mph/s
  4. It depends on how much time has elapsed.
9. 
Abe is helping to inform people about an upcoming election. He goes door to door, giving out information about the election. He usually visits about 10 houses an hour. He has already been out canvassing for 3 hours, but will stay out longer. Does the function [math]H(t) = 30 + 3t[/math] correctly represent the total number of houses Abe will visit, where [math]t[/math] is the additional time he will work today? If not, why not?
  1. Yes, this function correctly models this situation.
  2. No, the constant term should be 3, not 30, since he has only been out for 3 hours.
  3. No, the variable [math]H[/math] should be measuring how successful he is in convincing people to vote, not simply measuring how many houses he has visited.
  4. No, the coefficient of [math]t[/math] should be 10, since he can visit 10 houses per hour.
10. 
Kyle is an avid bird watcher, and is trying to spot some of the more rare birds in his area. He has already seen 8. However, it has taken 8 months to spot these birds. Kyle's friend is also a bird watcher, and says he typically sees 4 rare birds a month in a large forest outside the town. If Kyle decides to try looking for birds at the forest outside of town, is the linear function [math]B(m) = 2 + 4m[/math] correct in predicting the total number of rare birds, [math]B[/math], he will have seen in [math]m[/math] months time? If not, why not?
  1. Yes, this function is correct.
  2. No. Kyle has already seen 8 birds, so the constant term should be 8, not 2.
  3. No, since the rate at which Kyle sees birds is incorrect. He has seen 8 birds over 8 months. This means the coefficient of [math]m[/math] should be 1, not 4.
  4. No, the equation should be [math]B(m) = 4 + 2m[/math], since 4 represents the number of birds already seen (divided by 2 to account for the 2 sites, the park and the forest), and 2 rare birds per month is the rate at which he will probably see more rare birds.

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