Question

Richard is making copies of old family videos on DVDs for his entire family. The number of DVDs Richard can copy is directly proportional to the number of days that have passed. The table below shows the number of copies he has made so far. What is the constant of variation in the function that models the number of DVDs Richard can make as a function of time in days?

Answer 1

The constant of variation in a direct variation problem is found by dividing the number of DVDs made by the number of days passed. Once we have a pair of values from the provided table, we can calculate this constant to find out how many DVDs can be copied per day.

Step-by-step explanation:

The student is asking about the constant of variation which is a key concept in direct variation problems where one quantity varies directly as another. The function that models the number of DVDs Richard can make as a function of time is assumed to have the form y = kx, where y is the total number of DVDs, x is the number of days, and k is the constant of variation we need to find.

To find k, we need at least one pair of values for x and y. Since the table that would provide this data is not included in the question, the student will need to refer to this table and find two corresponding values, say y DVDs made in x days. Using these values, they would calculate k = y/x.

For example, if Richard made 10 DVDs in 2 days, then we would compute the constant of variation as k = 10 DVDs / 2 days = 5 DVDs/day. This constant tells us how many DVDs Richard can copy per day.