Which of the following scenarios can be modeled by a linear function?(1 point)

Question

Responses

the total pay of a person whose rate of pay per hour depends on the type of job
the total pay of a person whose rate of pay per hour depends on the type of job

the total pay of a person whose rate of pay per hour varies depending on the number of hours worked per week
the total pay of a person whose rate of pay per hour varies depending on the number of hours worked per week

the total pay of a person whose rate of pay per hour is fixed at $15 per hour
the total pay of a person whose rate of pay per hour is fixed at $15 per hour

the total pay of a person whose rate of pay per hour varies based on the difficulty of the job

Answer 1

To determine which scenario can be modeled by a linear function, we need to look for relationships where one variable changes in direct proportion to another.

1. The total pay of a person whose rate of pay per hour depends on the type of job - This generally does not represent a linear function because the rate can be different for different jobs, creating a non-linear relationship.

2. The total pay of a person whose rate of pay per hour varies depending on the number of hours worked per week - This scenario can also be non-linear if the rate increases with more hours worked or if there are tiered pay rates. Thus, it may not always be modeled by a linear function.

3. The total pay of a person whose rate of pay per hour is fixed at $15 per hour - This scenario can be modeled by a linear function since the total pay is directly proportional to the number of hours worked (Total Pay = Rate × Hours = $15 × Hours). This is a clear linear relationship.

4. The total pay of a person whose rate of pay per hour varies based on the difficulty of the job - Similar to the first scenario, this usually does not represent a linear function because variability based on job difficulty could lead to non-linear pay structures.

Therefore, the scenario that can be modeled by a linear function is:

The total pay of a person whose rate of pay per hour is fixed at $15 per hour.

Answer 2

Which one of the following scenarios can be modeled by a linear function?(1 point)
Responses

The total distance traveled by a biker if the biker rides a different number of miles each day.
The total distance traveled by a biker if the biker rides a different number of miles each day.

The total distance traveled by a delivery truck if the speed varies based on traffic.
The total distance traveled by a delivery truck if the speed varies based on traffic.

The total cost of a bag of groceries if the bag contains many different items.
The total cost of a bag of groceries if the bag contains many different items.

The total cost of building a new home if the builder charges $300 per square foot.

Answer 3

To determine which scenario can be modeled by a linear function, we need to identify situations where one variable changes at a constant rate relative to another variable.

1. The total distance traveled by a biker if the biker rides a different number of miles each day. - This scenario does not describe a linear function because the distance varies from day to day and is not constant.

2. The total distance traveled by a delivery truck if the speed varies based on traffic. - This does not represent a linear function either, as varying speeds would affect the distance traveled in a non-linear manner.

3. The total cost of a bag of groceries if the bag contains many different items. - While the total cost can be computed based on the price of each individual item, it does not have a constant relationship, especially if items vary in price, making it potentially non-linear.

4. The total cost of building a new home if the builder charges $300 per square foot. - This scenario represents a linear function because the total cost is directly proportional to the number of square feet (Total Cost = $300 × Square Feet). The unit rate is constant, which defines a linear relationship.

Therefore, the scenario that can be modeled by a linear function is:

The total cost of building a new home if the builder charges $300 per square foot.

Answer 4

Which one of the following scenarios can be modeled by an exponential function?(1 point)
Responses

a population of bacteria that increases by 10 every hour
a population of bacteria that increases by 10 every hour

the total pay of a person who earns a different rate depending on the job
the total pay of a person who earns a different rate depending on the job

a population of bacteria that doubles every hour
a population of bacteria that doubles every hour

the total pay of a person who earns $15 per hour

Answer 5

To determine which scenario can be modeled by an exponential function, we need to identify situations where a quantity increases by a constant percentage or factor over a certain interval, rather than by a fixed amount.

1. A population of bacteria that increases by 10 every hour - This scenario represents a linear function because the population increases by a fixed amount (10) each hour.

2. The total pay of a person who earns a different rate depending on the job - This situation is too variable and does not follow a consistent multiplicative pattern, so it cannot be modeled as an exponential function.

3. A population of bacteria that doubles every hour - This scenario exhibits exponential growth, as the population increases by a factor of 2 each hour. This is a classic example of exponential growth.

4. The total pay of a person who earns $15 per hour - This is a linear scenario since the pay is constant and straightforwardly proportional to the number of hours worked.

Therefore, the scenario that can be modeled by an exponential function is:

A population of bacteria that doubles every hour.

Answer 6

A research assistant observes that something is causing mice to die in the lab. The following table lists the number of mice at the end of each week.

Week 1 2 3 4 5
Number of mice 380 355 330 305 280
Determine whether the decreasing number of mice can be modeled by a linear decay function or an exponential decay function, and why.(1 point)
Responses

linear decay function; the number of mice decreases by 25% per week, which is a constant rate of change
linear decay function; the number of mice decreases by 25% per week, which is a constant rate of change

exponential decay function; the number of mice decreases by 25 per week, which is a constant percent rate of change
exponential decay function; the number of mice decreases by 25 per week, which is a constant percent rate of change

exponential decay function; the number of mice decreases by 75% per week, which is a constant percent rate of change
exponential decay function; the number of mice decreases by 75% per week, which is a constant percent rate of change

linear decay function; the number of mice decreases by 25 per week, which is a constant rate of change

Answer 7

To determine whether the decreasing number of mice can be modeled by a linear decay function or an exponential decay function, we need to analyze the rate at which the number of mice decreases.

Looking at the provided data:

• From Week 1 to Week 2: 380 to 355 (a decrease of 25 mice)
• From Week 2 to Week 3: 355 to 330 (a decrease of 25 mice)
• From Week 3 to Week 4: 330 to 305 (a decrease of 25 mice)
• From Week 4 to Week 5: 305 to 280 (a decrease of 25 mice)

The number of mice decreases by a constant amount of 25 mice per week, which indicates a constant rate of change. This means that the decrease is linear, not exponential.

Exponential decay would involve a percentage decrease, where the amount lost each week would depend on the current population size (e.g., a constant percentage of the remaining population).

Given this analysis, the correct response is:

Linear decay function; the number of mice decreases by 25 per week, which is a constant rate of change.

Answer 8

The table lists the value of a car each year after it is purchased.

Year 0 1 2 3 4
Value ($) 54,000 51,840 49,766 47,776 45,865
Determine whether the decreasing value can be modeled by a linear decay function or an exponential decay function, and why.

(1 point)
Responses

exponential decay function; the value decreases by $6,000 per year, which is a constant percent rate of change
exponential decay function; the value decreases by $6,000 per year, which is a constant percent rate of change

linear decay function; the value decreases by 96% per year, which is a constant percent rate of change
linear decay function; the value decreases by 96% per year, which is a constant percent rate of change

linear decay function; the value decreases by 0.96 per year, which is a constant percent rate of change
linear decay function; the value decreases by 0.96 per year, which is a constant percent rate of change

exponential decay function; the value decreases by 4% per year, which is a constant percent rate of change

Answer 9

To determine whether the decreasing value of the car can be modeled by a linear decay function or an exponential decay function, we need to analyze the rate of change in the value of the car over the years.

Here is the data provided:

| Year | Value ($) | |------|------------| | 0 | 54,000 | | 1 | 51,840 | | 2 | 49,766 | | 3 | 47,776 | | 4 | 45,865 |

Now let's calculate the change in value each year:

• From Year 0 to Year 1: \(54,000 - 51,840 = 2,160\)
• From Year 1 to Year 2: \(51,840 - 49,766 = 2,074\)
• From Year 2 to Year 3: \(49,766 - 47,776 = 1,990\)
• From Year 3 to Year 4: \(47,776 - 45,865 = 1,911\)

The decreases are not constant; they are diminishing each year. This suggests that the decrease is not linear.

To check if this could represent an exponential decay, we can calculate the percentage decrease each year relative to the previous year's value:

• From Year 0 to Year 1: \(\frac{2,160}{54,000} \approx 0.04\) or 4%
• From Year 1 to Year 2: \(\frac{2,074}{51,840} \approx 0.04\) or 4%
• From Year 2 to Year 3: \(\frac{1,990}{49,766} \approx 0.04\) or 4%
• From Year 3 to Year 4: \(\frac{1,911}{47,776} \approx 0.04\) or 4%

Since the percentage decrease remains roughly constant at about 4% each year, we can assert that the value of the car can be modeled by an exponential decay function.

The correct response is:

Exponential decay function; the value decreases by 4% per year, which is a constant percent rate of change.