Roger is using rehearsal to remember a telephone number. each time he repeats the numbers, he is "reentering" the information into his short-term memory, thus adding to the shelf life.

15 to 20 seconds

Explanation:

Since its primarily used to selection, initiation, and termination  of new information that we receive,  The short-term memory only capable in holding a small amount of information within a short period of time. The information in short term memory only last between 15-30 seconds (30 is the high end of the spectrum, average people only able to store it for 15 to 20 seconds). Keep repeating the information in our head will refresh the shelf life of this memory, adding a new 15-30 seconds every time we do so.

To move this memory into long-term memory, Roger could do either of these things:

1. Adding some sort of meaning to the information. Whether it's an emotional attachment or something that applicable in his previous long-term memory.

or

2. He could make himself encounter this information daily (such as looking at it every time he wakes up for the next couple of weeks)

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