A user is charged 300 monthly for a particular mobile plan, which includes 100 free text messages. Messages in excess of 100 are charged 1 each. Represent the amount a consumer pays each month in a function of the number of the messages m sent in a month
y = 300 for m <= 100
y = 300 + 1*m for m > 100
To represent the amount a consumer pays each month in terms of the number of messages sent, we can define a function. Let's say the function is C(m), where C represents the cost and m represents the number of messages sent.
To calculate the cost C(m), we need to consider two scenarios: when the number of messages sent is less than or equal to 100, and when it exceeds 100.
1. When m is less than or equal to 100:
In this case, all the messages are covered by the 100 free text messages included in the mobile plan. So the cost C(m) would be the fixed monthly charge of $300, represented as C(m) = 300.
2. When m exceeds 100:
When the number of messages exceeds 100, additional charges apply. For each excess message, the consumer is charged $1. So the cost C(m) in this case can be calculated as:
C(m) = 300 + (m - 100)
The term (m - 100) represents the number of excess messages beyond the 100 free messages. Multiplying it by $1 gives us the additional cost for those excess messages.
By combining both scenarios, the complete function C(m) can be represented as follows:
C(m) = 300, when m <= 100
C(m) = 300 + (m - 100), when m > 100
This function can be used to calculate the amount a consumer pays each month based on the number of messages sent.
To represent the amount a consumer pays each month in a function of the number of messages sent, let's break it down step by step:
Step 1: Determine the number of messages sent in excess of 100.
- Let's define the variable x as the number of messages sent in excess of 100.
- The total number of messages sent in a month would be m - 100, where m is the total number of messages sent.
Step 2: Calculate the additional cost for messages sent in excess of 100.
- Each message sent in excess of 100 is charged $1.
- So, the cost for messages sent in excess of 100 would be x dollars.
Step 3: Calculate the total monthly payment.
- The monthly payment is $300, which includes the cost for 100 free text messages.
- The additional cost for messages sent in excess of 100 is x dollars.
- Therefore, the total monthly payment can be represented as a function of the number of messages m sent:
- f(m) = $300 + x, where x = (m - 100)
To summarize, the amount a consumer pays each month can be represented by the function f(m) = $300 + (m - 100), where m is the number of messages sent in a month.