A user is charged php300 monthly for a particular mobile plan, which includes 100 free text messages. Messages in excess of 100 are charged php1 each. Represent the amount as a function of the number of messages m sent in a month.expressed by the piecewise function.
cost = {300 , m ≤ 100
= 300 + 100(m-100) , m> 100} , where m is the number of messages.
rewrite the piecewise function in the way you were taught.
Your cellphone plan costs Php 750 per month which includes free 500 texts. For every text message in excess of the 500 included in the plan, you are charged 10 centavos. Represent this into a function in equation form. *
Sure, here's a piecewise representation of the amount charged (A) as a function of the number of messages sent (m) in a month:
A(m) = 300 if m ≤ 100
A(m) = 300 + (m - 100) if m > 100
Why did the cell phone go to the eye doctor?
Because it lost all its contacts!
To represent the amount as a function of the number of messages sent in a month, we can use a piecewise function.
Let's break it down into two cases:
Case 1: Number of messages is less than or equal to 100 (m ≤ 100)
In this case, the amount charged will be a fixed monthly fee of php300, since the 100 free text messages are already included. So the function for this case is:
f(m) = 300
Case 2: Number of messages is greater than 100 (m > 100)
In this case, the amount charged will be the fixed monthly fee of php300 plus the charges for the additional messages. Each additional message is charged php1, so the total charge for the excess messages will be (m - 100). So the function for this case is:
f(m) = 300 + (m - 100)
Combining both cases, the piecewise function for the amount charged as a function of the number of messages sent in a month would be:
f(m) = 300 (if m ≤ 100)
f(m) = 300 + (m - 100) (if m > 100)
To represent the amount as a function of the number of messages sent in a month, we need to consider the different scenarios based on the number of messages.
Let's break it down into two cases:
Case 1: Number of messages (m) is less than or equal to 100:
In this case, since the user gets 100 free text messages, there will be no additional charges. The amount paid will be the fixed monthly charge of Php300.
So, for m ≤ 100, the amount function will be: f(m) = 300.
Case 2: Number of messages (m) is greater than 100:
In this case, the user has exceeded the 100 free text messages and will be charged Php1 for each additional message. Therefore, the amount paid will include the fixed monthly charge of Php300 plus an additional charge of Php1 per message in excess of 100. Since the number of additional messages is (m-100), the additional charge will be (m-100) multiplied by Php1.
So, for m > 100, the amount function will be: f(m) = 300 + (m - 100).
Combining both cases, we can write the piecewise function to represent the amount as a function of the number of messages sent:
f(m) = 300 for m ≤ 100
f(m) = 300 + (m - 100) for m > 100