Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To solve this problem, we need to clearly define the charges based on Andrew's cell phone plan using a piecewise function.
Let's break down Andrew's cell phone plan:
1. If Andrew uses up to 300 minutes in a month, he only pays a flat rate of [tex]$19. 2. For every minute over 300, Andrew pays an additional $[/tex]0.39 per minute.
Now let's look at the options given to see which one matches this scenario.
### Step-by-step Analysis of Each Option
#### Option A
[tex]\[ f(x) = \begin{cases} 19 & \text{if } x > 300 \\ 19 + 39x & \text{if } x \leq 300 \end{cases} \][/tex]
- This option states that if Andrew uses more than 300 minutes, the cost will be [tex]$19. However, this is incorrect because for more than 300 minutes, additional charges apply. - For \( x \leq 300 \), the function claims the cost is \( 19 + 39x \), which is incorrect because the flat rate of $[/tex]19 applies, not a multiplication.
#### Option B
[tex]\[ f(x) = \begin{cases} 19 & \text{if } x \leq 300 \\ 19 + 0.39(x - 300) & \text{if } x > 300 \end{cases} \][/tex]
- For [tex]\( x \leq 300 \)[/tex], the cost is correctly given as [tex]$19. - For \( x > 300 \), the cost is calculated as the base $[/tex]19 plus [tex]$0.39 for each minute over 300, which is indeed \( 19 + 0.39(x - 300) \). This option looks correct, let's check the rest. #### Option C \[ f(x) = \begin{cases} 19 & \text{if } x \leq 300 \\ 19 + 39x & \text{if } x > 300 \end{cases} \] - For \( x \leq 300 \), the cost is correctly $[/tex]19.
- For [tex]\( x > 300 \)[/tex], the function says the cost is [tex]\( 19 + 39x \)[/tex], which incorrectly multiplies the extra minutes by 39 instead of multiplying by 0.39 per extra minute.
#### Option D
[tex]\[ f(x) = \begin{cases} 19 & \text{if } x \leq 300 \\ 39x & \text{if } x > 300 \end{cases} \][/tex]
- For [tex]\( x \leq 300 \)[/tex], the cost is [tex]$19 which is correct. - For \( x > 300 \), the function says the cost is \( 39x \), which implies multiplying all the minutes by 39, ignoring the initial 300 minutes of $[/tex]19.
### Conclusion
Option B correctly reflects the structure of the cell phone plan. For [tex]\( x \leq 300 \)[/tex], the cost is [tex]$19, and for \( x > 300 \), the cost is the base $[/tex]19 plus $0.39 for each minute over 300. Therefore, the correct piecewise function that represents the charges based on Andrew's cell phone plan is:
[tex]\[ f(x) = \begin{cases} 19 & \text{if } x \leq 300 \\ 19 + 0.39(x - 300) & \text{if } x > 300 \end{cases} \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
Let's break down Andrew's cell phone plan:
1. If Andrew uses up to 300 minutes in a month, he only pays a flat rate of [tex]$19. 2. For every minute over 300, Andrew pays an additional $[/tex]0.39 per minute.
Now let's look at the options given to see which one matches this scenario.
### Step-by-step Analysis of Each Option
#### Option A
[tex]\[ f(x) = \begin{cases} 19 & \text{if } x > 300 \\ 19 + 39x & \text{if } x \leq 300 \end{cases} \][/tex]
- This option states that if Andrew uses more than 300 minutes, the cost will be [tex]$19. However, this is incorrect because for more than 300 minutes, additional charges apply. - For \( x \leq 300 \), the function claims the cost is \( 19 + 39x \), which is incorrect because the flat rate of $[/tex]19 applies, not a multiplication.
#### Option B
[tex]\[ f(x) = \begin{cases} 19 & \text{if } x \leq 300 \\ 19 + 0.39(x - 300) & \text{if } x > 300 \end{cases} \][/tex]
- For [tex]\( x \leq 300 \)[/tex], the cost is correctly given as [tex]$19. - For \( x > 300 \), the cost is calculated as the base $[/tex]19 plus [tex]$0.39 for each minute over 300, which is indeed \( 19 + 0.39(x - 300) \). This option looks correct, let's check the rest. #### Option C \[ f(x) = \begin{cases} 19 & \text{if } x \leq 300 \\ 19 + 39x & \text{if } x > 300 \end{cases} \] - For \( x \leq 300 \), the cost is correctly $[/tex]19.
- For [tex]\( x > 300 \)[/tex], the function says the cost is [tex]\( 19 + 39x \)[/tex], which incorrectly multiplies the extra minutes by 39 instead of multiplying by 0.39 per extra minute.
#### Option D
[tex]\[ f(x) = \begin{cases} 19 & \text{if } x \leq 300 \\ 39x & \text{if } x > 300 \end{cases} \][/tex]
- For [tex]\( x \leq 300 \)[/tex], the cost is [tex]$19 which is correct. - For \( x > 300 \), the function says the cost is \( 39x \), which implies multiplying all the minutes by 39, ignoring the initial 300 minutes of $[/tex]19.
### Conclusion
Option B correctly reflects the structure of the cell phone plan. For [tex]\( x \leq 300 \)[/tex], the cost is [tex]$19, and for \( x > 300 \), the cost is the base $[/tex]19 plus $0.39 for each minute over 300. Therefore, the correct piecewise function that represents the charges based on Andrew's cell phone plan is:
[tex]\[ f(x) = \begin{cases} 19 & \text{if } x \leq 300 \\ 19 + 0.39(x - 300) & \text{if } x > 300 \end{cases} \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
