Question

the graph shows the number of laundry pods p used during t months. the relationship between time and the number of laundry pods used is proportional.
part a
what does the point (1, 12) mean in this situation?
part b
enter an equation to represent the total number of laundry pods p used in t months.
part c
a bag contains 100 laundry pods. in what month will the last laundry pod be used? select from the drop - down list to make the statement true.
the last laundry pod will be used in the select month month.

Explanation:

Step1: Interpret the point (1, 12)

In the context of the problem, the first - coordinate represents time and the second - coordinate represents the number of laundry pods. So, in 1 month, 12 laundry pods are used.

Step2: Find the equation of the proportional relationship

Since the relationship between the number of laundry pods \(p\) and time \(t\) is proportional, the equation is of the form \(p = kt\), where \(k\) is the constant of proportionality. From the point \((1,12)\), when \(t = 1\) and \(p=12\), we find that \(k = 12\). So the equation is \(p = 12t\).

Step3: Find the month when 100 pods are used

We set \(p = 100\) in the equation \(p = 12t\). Then \(12t=100\), and \(t=\frac{100}{12}=\frac{25}{3}\approx8.33\). Since we are talking about months, in the 9th month the last laundry pod will be used.

Answer:

Part A: In 1 month, 12 laundry pods are used.
Part B: \(p = 12t\)
Part C: 9