Alice is hosting her extended family for Christmas lunch, so she is busy cooking on Christmas Eve. She wants to get to bed though as she knows Christmas day will be busy! The pot of soup has finally boiled (at 100°C), but Alice is concerned about putting hot food straight in the fridge. She decides to cool the pot off in a sink full of cold water (at 5°C). This table shows the temperature of the soup over a period of 75 minutes. 0 100 5 83.56266539 10 69.96939362 15 58.72809191 20 49.43181166 25 41.74401634 30 35.38639853 35 30.12880485 40 25.78090407 45 22.18529698 50 19.21181828 55 16.75282447 60 14.71929701 65 13.03761978 70 11.64691403 75 10.49683456 1. Draw a graph of information in the table (note: you can use DESMOS to do so). 2. Use the graph to figure out how long Alice needs to wait for the soup to cool down to 20°C.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Alice is hosting her extended family for Christmas lunch, so she is busy cooking on Christmas Eve. She wants to get to bed though as she knows Christmas day will be busy!
The pot of soup has finally boiled (at 100°C), but Alice is concerned about putting hot food straight in the fridge.
She decides to cool the pot off in a sink full of cold water (at 5°C). This table shows the temperature of the soup over a period of 75 minutes.
| 0 | 100 |
| 5 | 83.56266539 |
| 10 | 69.96939362 |
| 15 | 58.72809191 |
| 20 | 49.43181166 |
| 25 | 41.74401634 |
| 30 | 35.38639853 |
| 35 | 30.12880485 |
| 40 | 25.78090407 |
| 45 | 22.18529698 |
| 50 | 19.21181828 |
| 55 | 16.75282447 |
| 60 | 14.71929701 |
| 65 | 13.03761978 |
| 70 | 11.64691403 |
| 75 | 10.49683456 |
1. Draw a graph of information in the table (note: you can use DESMOS to do so).
2. Use the graph to figure out how long Alice needs to wait for the soup to cool down to 20°C.
3. Explain why an exponential model is the most appropriate fit for this scenario.
4. Find the equation for the exponential model of the type ? = ? + ? × ?? (note: you can use DESMOS to do this).
5. Looking at the graph, what do you think will happen to the temperature of the pot eventually?
6. How could you use the equation ?(?) = 5 + 95 × (0.963)? to justify your answer to question 5?
7. Explain how you can use the graph to work out what temperature the soup will be after 1 hour.
8. Show how you can use the equation to work out what temperature the soup will be after 1 hour.
9. Confirm the solution to question 8 using the algebraic method.
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