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

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

Answer 1

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.

In this case, the total pay (y) can be expressed as a linear function of the number of hours worked (x) with the equation \( y = 15x \), where 15 is the fixed hourly rate.

The other scenarios involve varying rates of pay based on different conditions, which would not produce a linear function.

Answer 2

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

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

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

Answer 3

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.

In this case, the total cost (C) can be expressed as a linear function of the square footage (S) with the equation \( C = 300S \), where 300 is the cost per square foot.

The other scenarios involve varying factors (speed and distance for the delivery truck, the number and types of items in a grocery bag, and daily distances for the biker) that would not produce a linear relationship.

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

Answer 5

The scenario that can be modeled by an exponential function is:

a population of bacteria that doubles every hour.

In this case, the population (P) can be expressed as an exponential function, where the population at time \( t \) can be modeled by the equation \( P(t) = P_0 \cdot 2^t \), with \( P_0 \) being the initial population and \( t \) being the number of hours.

The other scenarios describe linear growth or different payment rates, which do not follow an exponential pattern.

Answer 6

Use the table to answer the question.

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

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

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

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

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 changes in the number of mice over the weeks.

From the table:

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

The number of mice decreases by 25 each week, which is a constant amount. This indicates a constant rate of change.

Thus, 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

Use the table to answer the question.

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 4% 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

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 $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

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 changes in the value of the car each year.

Here are the values given in the table:

• Year 0: $54,000
• Year 1: $51,840
• Year 2: $49,766
• Year 3: $47,776
• Year 4: $45,865

Let's check the percent change from year to year:

1. Year 0 to Year 1: \[ \frac{51,840 - 54,000}{54,000} \approx -0.04 \quad \text{(decrease of 4%)} \]

2. Year 1 to Year 2: \[ \frac{49,766 - 51,840}{51,840} \approx -0.04 \quad \text{(decrease of about 4%)} \]

3. Year 2 to Year 3: \[ \frac{47,776 - 49,766}{49,766} \approx -0.04 \quad \text{(decrease of about 4%)} \]

4. Year 3 to Year 4: \[ \frac{45,865 - 47,776}{47,776} \approx -0.04 \quad \text{(decrease of about 4%)} \]

Each year, the value of the car decreases consistently by approximately 4%. This indicates a constant percentage rate of decline, which is characteristic of exponential decay.

Therefore, the correct response is:

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