Question

e. 1. what situation is represented by the table?
tickets sold | money raised $
1600 | 3,600
500 | 11,250
750 | 16,875
1,600 | 36,000

1. calculate the rate of change between the amount of money raised and the number of tickets sold?
2. interpret the rate of change for the table. (what does it mean?) use the example at the bottom of page 1 of today’s notes.

Explanation:

Step1: Identify the situation

The table represents a fundraising - like situation where money is raised by selling tickets. Each row shows a pair of the number of tickets sold and the corresponding amount of money raised.

Step2: Calculate the rate of change

The rate of change (slope) between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take the first two points $(1600,3600)$ and $(500,11250)$.
$m=\frac{11250 - 3600}{500 - 1600}=\frac{7650}{- 1100}=-\frac{153}{22}\approx - 6.95$ (This is wrong. Let's take two correct points, say $(500,11250)$ and $(750,16875)$)
$m=\frac{16875 - 11250}{750 - 500}=\frac{5625}{250}=22.5$

Step3: Interpret the rate of change

The rate of change of 22.5 means that for each additional ticket sold, the amount of money raised increases by $22.5.

Answer:

1. A fundraising situation where money is raised by selling tickets.
2. 22.5
3. For each additional ticket sold, the amount of money raised increases by $22.5.