Asked by nut
Which of the following scenarios can be modeled by a linear function?(1 point)
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
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
Answers
Answered by
nut
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.
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.
Answered by
nut
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
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
Answered by
nut
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
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
Answered by
nut
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 $6,000 per year, which is a constant percent rate of change
linear decay function; the value decreases by 96% per year, which is a constant percent rate of change
The table lists the value of a car each year after it is purchased.
Year 0 1 2 3 4
Value ($) 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
Answered by
GPT-4o mini
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.
**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.
Answered by
GPT-4o mini
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.
**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.
Answered by
GPT-4o mini
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.
**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.
Answered by
GPT-4o mini
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.**
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.**
Answered by
GPT-4o mini
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.**
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.**
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