Question
6. Select all representations for the domain of a function given by the number of hours slept in one day.
A) {x| x ∈ R}
B) [0, 24]
C) [0, ∞)
D) (24, ∞)
E) (0, 24)
F) {x| x > 24}
G) {x | 0 ≤ x ≤ 24}
9. A car has 86,391 miles on its odometer and accumulates an average of 260 more each week. What is the function rule that represents the total number of M miles the car will have on the odometer after w weeks?
A) M(w) = 86,391 + 260w
B) M(w) = 86,391w + 260
C) M(w) = 86,391w + 260w
D) M(w) = 86,391 + 260
10. The value of a motorcycle changes according to the equation V(t) = 5,000(1.03)^t, where V(t) = value in dollars and t = time in years.
Use the dropdowns to complete the statements.
In the equation, the number 5,000 represents the ________ of the motorcycle.
A) final rate
B) growth rate
C) initial rate
What does V(t) = 9000 mean in the context of this problem?
A) The initial value of the motorcycle is $9000.
B) The rate at which it takes the motorcycle to be worth $9000.
C) The value of the motorcycle is $9000.
D) The time it takes for the motorcycle's value to be $9000.
What does a value of t = 3 mean in the context of this problem?
A) Time being three years before the motorcycle was given an initial value.
B) Time being three years after the motorcycle was given an initial value.
C) The time is takes for the value to be $5000.
D) It will take three years for the motorcycle's value to depreciate.
A) {x| x ∈ R}
B) [0, 24]
C) [0, ∞)
D) (24, ∞)
E) (0, 24)
F) {x| x > 24}
G) {x | 0 ≤ x ≤ 24}
9. A car has 86,391 miles on its odometer and accumulates an average of 260 more each week. What is the function rule that represents the total number of M miles the car will have on the odometer after w weeks?
A) M(w) = 86,391 + 260w
B) M(w) = 86,391w + 260
C) M(w) = 86,391w + 260w
D) M(w) = 86,391 + 260
10. The value of a motorcycle changes according to the equation V(t) = 5,000(1.03)^t, where V(t) = value in dollars and t = time in years.
Use the dropdowns to complete the statements.
In the equation, the number 5,000 represents the ________ of the motorcycle.
A) final rate
B) growth rate
C) initial rate
What does V(t) = 9000 mean in the context of this problem?
A) The initial value of the motorcycle is $9000.
B) The rate at which it takes the motorcycle to be worth $9000.
C) The value of the motorcycle is $9000.
D) The time it takes for the motorcycle's value to be $9000.
What does a value of t = 3 mean in the context of this problem?
A) Time being three years before the motorcycle was given an initial value.
B) Time being three years after the motorcycle was given an initial value.
C) The time is takes for the value to be $5000.
D) It will take three years for the motorcycle's value to depreciate.
Answers
GPT-4o mini
**6. Select all representations for the domain of a function given by the number of hours slept in one day.**
The valid representations for the domain of hours slept in one day (which can range from 0 to 24 hours, inclusive) are:
- **B) [0, 24]** - This includes all possible hours from 0 to 24.
- **G) {x | 0 ≤ x ≤ 24}** - This is another way to express the range from 0 to 24.
The other options are not suitable:
- A) {x| x ∈ R} includes negative values, which are not applicable to hours slept.
- C) [0, ∞) includes values greater than 24, which are not possible.
- D) (24, ∞) includes only values greater than 24, which are not possible.
- E) (0, 24) excludes 0 and 24, which can actually be the bounds.
- F) {x| x > 24} includes values outside the possible range.
Therefore, the correct answers are **B** and **G**.
---
**9. A car has 86,391 miles on its odometer and accumulates an average of 260 more each week. What is the function rule that represents the total number of M miles the car will have on the odometer after w weeks?**
The function rule that represents the total number of miles after w weeks is:
- **A) M(w) = 86,391 + 260w** - This correctly indicates the initial mileage plus the additional miles accumulated over w weeks.
The other options do not accurately represent the relationship as specified.
---
**10. The value of a motorcycle changes according to the equation V(t) = 5,000(1.03)^t, where V(t) = value in dollars and t = time in years.**
- In the equation, the number 5,000 represents the **C) initial rate** of the motorcycle.
- What does V(t) = 9000 mean in the context of this problem?
- **C) The value of the motorcycle is $9000.** - This indicates the current value of the motorcycle at a particular time.
- What does a value of t = 3 mean in the context of this problem?
- **B) Time being three years after the motorcycle was given an initial value.** - This indicates that t represents time elapsed in years since the initial value was set.
To summarize:
- **Initial rate** is **C**.
- **V(t) = 9000** is **C**.
- **t = 3** is **B**.
The valid representations for the domain of hours slept in one day (which can range from 0 to 24 hours, inclusive) are:
- **B) [0, 24]** - This includes all possible hours from 0 to 24.
- **G) {x | 0 ≤ x ≤ 24}** - This is another way to express the range from 0 to 24.
The other options are not suitable:
- A) {x| x ∈ R} includes negative values, which are not applicable to hours slept.
- C) [0, ∞) includes values greater than 24, which are not possible.
- D) (24, ∞) includes only values greater than 24, which are not possible.
- E) (0, 24) excludes 0 and 24, which can actually be the bounds.
- F) {x| x > 24} includes values outside the possible range.
Therefore, the correct answers are **B** and **G**.
---
**9. A car has 86,391 miles on its odometer and accumulates an average of 260 more each week. What is the function rule that represents the total number of M miles the car will have on the odometer after w weeks?**
The function rule that represents the total number of miles after w weeks is:
- **A) M(w) = 86,391 + 260w** - This correctly indicates the initial mileage plus the additional miles accumulated over w weeks.
The other options do not accurately represent the relationship as specified.
---
**10. The value of a motorcycle changes according to the equation V(t) = 5,000(1.03)^t, where V(t) = value in dollars and t = time in years.**
- In the equation, the number 5,000 represents the **C) initial rate** of the motorcycle.
- What does V(t) = 9000 mean in the context of this problem?
- **C) The value of the motorcycle is $9000.** - This indicates the current value of the motorcycle at a particular time.
- What does a value of t = 3 mean in the context of this problem?
- **B) Time being three years after the motorcycle was given an initial value.** - This indicates that t represents time elapsed in years since the initial value was set.
To summarize:
- **Initial rate** is **C**.
- **V(t) = 9000** is **C**.
- **t = 3** is **B**.