Question

You start a daily flower club and charge \(\$ 10\) to join and \(\$ .50\) per day. Every day each member of the club gets a fresh flower. Let \(n\) represent the number of club members and let \(I\) represent your income for four weeks. A model for the situation is \(I=[10+4 \cdot 7(0.5)] n .\) Write an input-output table that shows your income for \(2,4,6,8,\) and 10 club members.

Short answer

The income for 2, 4, 6, 8, and 10 members would be 48, 96, 144, 192, and 240 respectively

Step-by-step solution

Understand and simplify the income model

The model of the given situation is \(I = [10 + 4 \cdot 7(0.5)]n\). This formula can be simplified as \(I = [10 + 14]n\), which is \(I = 24n\). So, for any given number of \(n\) members, the income \(I\) would be \(24n\).

From the simplified model, compute the income for 2 members

To find the income for 2 members, substitute \(n=2\) into the simplified model equation: \(I = 24(2) = 48\)

Compute the income for 4 members

To find the income for 4 members, substitute \(n=4\) into the equation: \(I = 24(4) = 96\)

Compute the income for 6 members

To find the income for 6 members, substitute \(n=6\) into the equation: \(I = 24(6) = 144\)

Compute the income for 8 members

To find the income for 8 members, substitute \(n=8\) into the equation: \(I = 24(8) = 192\)

Compute the income for 10 members

To find the income for 10 members, substitute \(n=10\) into the equation: \(I = 24(10) = 240\)