Final Answer:
The constant of variation in the function representing the number of DVDs Richard can make as a function of time in days is typically denoted as k in a direct variation equation.
Step-by-step explanation:
In a direct variation equation of the form y = kx, where y represents the number of DVDs made, x represents time in days, and k is the constant of variation, k signifies the rate at which DVDs are produced per day. This constant remains consistent throughout the function; it signifies the ratio of DVDs produced to the time taken.
For instance, if Richard can produce 5 DVDs per day, then the direct variation equation becomes y = 5x, where y represents the total number of DVDs made and x represents the number of days. Here, 5 is the constant of variation, indicating that for every additional day, 5 more DVDs are made.
This constant of variation is crucial for predicting the number of DVDs Richard can produce given any specific duration of time. By multiplying the constant of variation by the number of days, the total number of DVDs produced within that time frame can be determined accurately. It remains a fixed rate throughout the function, showcasing the consistent relationship between time and DVD production.