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Sam goes on a diet - AQA - A-Level Maths Pure - Question 6 - 2017 - Paper 1
Question 6
Sam goes on a diet. He assumes that his mass, m kg after t days, decreases at a rate that is inversely proportional to the cube root of his mass. (a) Construct a di... show full transcript
Worked Solution & Example Answer:Sam goes on a diet - AQA - A-Level Maths Pure - Question 6 - 2017 - Paper 1
Step 1
Construct a differential equation involving m, t and a positive constant k
Answer
To model the situation described, we need to represent the rate of change of Sam's mass, m, with respect to time, t. Given that this rate decreases inversely proportional to the cube root of his mass, we express this mathematically as:
Where:
- ( \frac{dm}{dt} ) represents the rate of change of mass,
- ( k ) is a positive constant,
- ( \sqrt[3]{m} ) denotes the cube root of his mass, indicating the inverse relationship.
Step 2
Explain why Sam’s assumption may not be appropriate
Answer
Sam's assumption may not be entirely accurate because the model suggests that his mass will continue to decrease indefinitely as time progresses. In reality, if he continues to eat, particularly if he has meals that are not strictly unhealthy, his mass may stabilize or even increase after initial weight loss periods. Additionally, physiological factors and changes in metabolism over time are not accounted for in this model.