James can store 8 GB of music on his phone. If a 3-min digital song requires 3.5 MB of storage space, what are the domain and range for the relationship between memory used and number of songs that are each 3 min in length?
8 GB = 8,000 MB.
8,000MB/(3.5MB/song) = 2285 Songs that can be stored in memory.
To find the domain and range for the relationship between memory used and the number of songs that are each 3 minutes in length, we need to consider the storage capacity of James' phone and the amount of memory each song requires.
Let's start with the domain. The domain represents the set of all possible inputs or values that the independent variable (number of songs) can take.
In this case, the number of songs can be any positive whole number since it doesn't make sense to have a fraction or negative number of songs. So, the domain is all positive integers: {1, 2, 3, 4, ...}.
Next, let's determine the range. The range represents the set of all possible outputs or values that the dependent variable (memory used) can take.
A 3-minute digital song requires 3.5 MB of storage space. To find the range, we need to consider how many songs can fit within James' 8 GB (or 8000 MB) storage capacity. We can calculate this by dividing the total storage capacity by the memory required for each song:
8000 MB ÷ 3.5 MB/song ≈ 2285.71 songs
Since we can't have a fractional number of songs, the maximum number of songs that can fit in James' phone would be 2285 songs.
Therefore, the range would be all whole numbers from 1 to 2285: {1, 2, 3, ..., 2285}.
So, the domain is {1, 2, 3, 4, ...} and the range is {1, 2, 3, ..., 2285}.