Question

1. a shop rents bicycles to customers. the rental cost is based on the length of time the bicycle is rented. the graph shows the costs of five bicycle rentals. the relationship between time and rental cost is proportional.

part a
complete the table by using the times and rental costs from the graph.
bicycle rental costs

Explanation:

Step1: Identify the proportional relationship

Since the relationship between time \(t\) (in hours) and rental cost \(C\) (in dollars) is proportional, we can use the formula \(C = kt\), where \(k\) is the constant of proportionality. We can find \(k\) using the point \((2,5)\) (from the table where \(t = 2\) and \(C=5\)). Substituting into \(C = kt\), we get \(5=k\times2\), so \(k=\frac{5}{2}=2.5\).

Step2: Calculate the rental cost for \(t = 0.5\)

Using \(C = kt\) with \(k = 2.5\) and \(t=0.5\), we have \(C=2.5\times0.5=\frac{2.5}{2}=1.25\)

Step3: Calculate the rental cost for \(t = 1\)

Using \(C = kt\) with \(k = 2.5\) and \(t = 1\), we have \(C=2.5\times1 = 2.5\)

Step4: Calculate the time for \(C = 3\)

Using \(C = kt\) and solving for \(t\), we get \(t=\frac{C}{k}\). Substituting \(C = 3\) and \(k = 2.5\), we have \(t=\frac{3}{2.5}=\frac{3\times2}{2.5\times2}=\frac{6}{5}=1.2\)

Step5: Calculate the time for \(C = 5\)

Using \(C = kt\) and solving for \(t\), with \(C = 5\) and \(k = 2.5\), we have \(t=\frac{5}{2.5}=2\)

Step6: Calculate the rental cost for \(t = 3\)

Using \(C = kt\) with \(k = 2.5\) and \(t = 3\), we have \(C=2.5\times3=7.5\)

Answer:

Time (hours)	Rental Cost (dollars)
\(1\)	\(2.5\)
\(1.2\)	\(3.00\)
\(2\)	\(5.00\)
\(3\)	\(7.5\)