Question 24 (4 marks) There are two tanks on a property, Tank $A$ and $\operatorname{Tank} B$. Initially, Tank $A$ holds 1000 litres of water and Tank $B$ is empty. (a) Tank $A$ begins to lose water at a constant rate of 20 litres per minute. The volume 1 of water in Tank $A$ is modelled by $V=1000-20 t$ where $V$ is the volume in litres and $t$ is the time in minutes from when the tank begins to lose water. On the grid below, draw the graph of this model and label it as Tank $A$. $100-(20 \times 20)+$ Question 24 continues on page 21
Solution
Step 1 ：The problem provides us with the equation \(V=1000-20t\), where \(V\) is the volume of water in Tank A in litres and \(t\) is the time in minutes from when the tank begins to lose water.
Step 2 ：Tank A starts with 1000 litres of water and loses water at a constant rate of 20 litres per minute.
Step 3 ：We can generate a list of volumes for each minute over a 60 minute period using the given equation. The volumes are: [1000, 980, 960, 940, 920, 900, 880, 860, 840, 820, 800, 780, 760, 740, 720, 700, 680, 660, 640, 620, 600, 580, 560, 540, 520, 500, 480, 460, 440, 420, 400, 380, 360, 340, 320, 300, 280, 260, 240, 220, 200, 180, 160, 140, 120, 100, 80, 60, 40, 20, 0, -20, -40, -60, -80, -100, -120, -140, -160, -180, -200].
Step 4 ：We can also generate a list of times for each minute over the same 60 minute period. The times are: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60].
Step 5 ：Plotting these values on a graph, we can visualize the decrease in volume over time.
Step 6 ：The graph shows a linear decrease in the volume of water in Tank A over time, starting from 1000 litres and decreasing at a rate of 20 litres per minute.
Step 7 ：After 50 minutes, the tank is empty. This is consistent with the given model \(V=1000-20t\).
Step 8 ：\(\boxed{\text{Final Answer: The graph shows a linear decrease in the volume of water in Tank A over time, starting from 1000 litres and decreasing at a rate of 20 litres per minute. After 50 minutes, the tank is empty.}}\)
