An upper-bound inequality fits a situation where each item uses a fixed amount and the total can be at most a limit. Multiply the amount per item by the number of items, then use a Desmos regression on the equality to find the cutoff. If the cutoff is a whole number and the limit includes equality, it counts; don't stop one item early.
Hints
- Hint 1
An inequality compares a possible total with a limit. If counts songs, each song adds the same amount of data. What expression gives the data used by songs, and which symbol means at most?
- Hint 2
The boundary is where the data used equals the daily limit. Find that equality in Desmos, then check whether the at-most limit allows Maya to use exactly that much data.
Step-by-step
Find the data limit per song
Step 1Turn the limit into an inequality
Let be the number of songs. Each song uses megabytes, so songs use megabytes. At most means Maya can use megabytes but cannot go over, so .
- Step 2
Find and interpret the cutoff
Type in Desmos. The asks Desmos to find the boundary where the data used equals the limit, and is the value it solves for. Under PARAMETERS, Desmos shows . When an at-most limit lands on a whole number, equality counts. Maya can download songs; one more would add megabytes and exceed the limit. Choice C.