Part 1: Come up with and describe two scenarios: one that models a direct variation situation and one that models an inverse variation situation. Do not state explicitly which scenario is which, but provide at least four data pairs for each situation. Your classmates will have to determine which of the scenarios is a direct variation and which is an inverse variation, and the value of k for each.
Part 2: View and comment on the work of at least two other students. Determine which of the scenarios is a direct variation and which is an inverse variation, and calculate the value of k for each. Be sure to explain how you knew that the situation was either a direct or inverse variation as well as any potential problems you might see or commendations that are deserved.
Part 1: Come up with and describe two scenarios: one that models a direct variation situation and one that models an inverse variation situation. Do not state explicitly which scenario is which, but provide at least four data pairs for each situation. Your classmates will have to determine which of the scenarios is a direct variation and which is an inverse variation, and the value of k for each.
Part 2: View and comment on the work of at least two other students. Determine which of the scenarios is a direct variation and which is an inverse variation, and calculate the value of k for each. Be sure to explain how you knew that the situation was either a direct or inverse variation as well as any potential problems you might see or commendations that are deserved.
2 answers
Scenario 1: The speed at which a car travels on a highway compared to the amount of time it takes to travel a certain distance.
Data pairs:
- Speed: 60 mph, Time: 2 hours
- Speed: 80 mph, Time: 1.5 hours
- Speed: 50 mph, Time: 3 hours
- Speed: 70 mph, Time: 2.5 hours
Scenario 2: The number of workers needed to complete a task compared to the amount of time it takes to complete the task.
Data pairs:
- Workers: 4, Time: 8 hours
- Workers: 5, Time: 6.4 hours
- Workers: 2, Time: 16 hours
- Workers: 8, Time: 4 hours
Part 2:
Student 1:
Scenario: "The amount of water used in a household compared to the number of people living in the household"
Data pairs:
- People: 2, Water usage: 500 gallons
- People: 4, Water usage: 1000 gallons
- People: 3, Water usage: 750 gallons
- People: 5, Water usage: 1250 gallons
I can tell that this is a direct variation because as the number of people in the household increases, so does the amount of water that is used. To find k, I can divide any of the pairs of data. For example:
500/2 = 250 = k
So the equation would be: water usage = 250 * number of people
Potential problem: It's important to note that there are other factors that could affect water usage beyond the number of people in a household, such as house size or water conservation practices.
Student 2:
Scenario: "The amount of money earned by a store compared to the number of customers that visit the store".
Data pairs:
- Customers: 200, Money earned: $4000
- Customers: 300, Money earned: $3000
- Customers: 100, Money earned: $6000
- Customers: 250, Money earned: $4500
I can tell that this is an inverse variation because as the number of customers in the store increases, the amount of money earned decreases. To find k, I can multiply any of the pairs of data. For example:
200 * 4000 = 800000 = k
So the equation would be: money earned = 800000/customers
Potential problem: There could be a variety of factors that affect the amount of money earned by a store beyond the number of customers, such as the prices of goods or overhead costs.
Data pairs:
- Speed: 60 mph, Time: 2 hours
- Speed: 80 mph, Time: 1.5 hours
- Speed: 50 mph, Time: 3 hours
- Speed: 70 mph, Time: 2.5 hours
Scenario 2: The number of workers needed to complete a task compared to the amount of time it takes to complete the task.
Data pairs:
- Workers: 4, Time: 8 hours
- Workers: 5, Time: 6.4 hours
- Workers: 2, Time: 16 hours
- Workers: 8, Time: 4 hours
Part 2:
Student 1:
Scenario: "The amount of water used in a household compared to the number of people living in the household"
Data pairs:
- People: 2, Water usage: 500 gallons
- People: 4, Water usage: 1000 gallons
- People: 3, Water usage: 750 gallons
- People: 5, Water usage: 1250 gallons
I can tell that this is a direct variation because as the number of people in the household increases, so does the amount of water that is used. To find k, I can divide any of the pairs of data. For example:
500/2 = 250 = k
So the equation would be: water usage = 250 * number of people
Potential problem: It's important to note that there are other factors that could affect water usage beyond the number of people in a household, such as house size or water conservation practices.
Student 2:
Scenario: "The amount of money earned by a store compared to the number of customers that visit the store".
Data pairs:
- Customers: 200, Money earned: $4000
- Customers: 300, Money earned: $3000
- Customers: 100, Money earned: $6000
- Customers: 250, Money earned: $4500
I can tell that this is an inverse variation because as the number of customers in the store increases, the amount of money earned decreases. To find k, I can multiply any of the pairs of data. For example:
200 * 4000 = 800000 = k
So the equation would be: money earned = 800000/customers
Potential problem: There could be a variety of factors that affect the amount of money earned by a store beyond the number of customers, such as the prices of goods or overhead costs.
1 answer