Final answer:
The graph representing k-cups usage over time is a linear decrease from 100 k-cups on day 0 to 0 k-cups on day 20. The equation y = 100 - 5x models this situation, where y is the number of k-cups left, and x is the number of days. After 6 days, an estimated 70 k-cups would be left.
Step-by-step explanation:
To graph the situation of k-cups usage over time, we start by understanding the given data: 100 k-cups last 20 days. This means that k-cups are used at a steady rate. To find this rate, we divide the total number of k-cups by the number of days they last:
Rate of use = Total k-cups / Number of days = 100 k-cups / 20 days = 5 k-cups/day
This rate tells us how many k-cups are used each day. Now we can sketch a graph where the x-axis represents the number of days, and the y-axis represents the number of k-cups remaining.
The graph starts at (0,100) since we have 100 k-cups at day 0, and it decreases linearly. After each day, we go down by 5 on the y-axis. Therefore, the point at day 20 would be (20,0), as all k-cups will have been used.
The equation that represents the situation is:
y = 100 - 5x
where 'y' is the number of k-cups left and 'x' is the number of days that have passed.
Estimating the number of k-cups left after 6 days:
y = 100 - 5(6) = 100 - 30 = 70
So, after 6 days, there would be an estimated 70 k-cups left.