Question

The maximum number of text messages Madison can send each month is 1,000. If Madison sends 18 text messages a day, write a function that represents the number of text messages, T(X), remaining after the xth day of the month.

Answer 1

A linear function T(X) = 1000 - 18X can represent the number of text messages remaining after the xth day of the month, where X is the number of days. The function can be used to find the number of text messages remaining after any given day.

Step-by-step explanation:

Let T(X) represent the number of text messages remaining after the xth day of the month. We know that Madison can send a maximum of 1,000 text messages each month. If Madison sends 18 text messages a day, we can use the linear function T(X) = 1000 - 18X to represent the number of text messages remaining after X days.

For example, after 1 day, Madison will have 1000 - 18(1) = 982 text messages remaining. After 2 days, Madison will have 1000 - 18(2) = 964 text messages remaining.

The student is asking to create a function T(x) that represents the number of text messages remaining after the xth day of the month, given a maximum of 1,000 messages and that Madison sends 18 text messages per day.

To determine this, you would subtract 18x from the total number of messages Madison can send each month. The function would therefore be T(x) = 1000 - 18x, where x represents the day of the month.

To find the number of text messages remaining after the xth day, simply substitute X with the number of days into the function T(X) = 1000 - 18X.