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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 rate of change of Sam's mass, we need to describe how his mass decreases over time. We know that the rate of change of mass can be represented as:
According to the problem, this decrease is inversely proportional to the cube root of his mass. Therefore, we can express this relationship mathematically as:
Here, k is a positive constant representing the rate of decrease. Thus, the differential equation that models Sam's mass over time is:
Step 2
Explain why Sam's assumption may not be appropriate
Answer
Sam's assumption may not accurately represent his situation because it implies a continuous decrease in mass regardless of external factors, such as dietary changes. For instance, if he consumes food, his mass could increase rather than decrease. Additionally, the model suggests that his mass will continually decrease indefinitely, which is unrealistic and may not reflect physiological limits and regulations of human metabolism.