Question

Consider the weight gain trajectory of a young sumo wrestler named Akebono, who embarked on a special high-calorie diet to rapidly gain weight. Initiating the diet at 90 kg, Akebono experienced a consistent linear rate of weight gain. After 8 months, his weight reached 138 kg.

Formulate a comprehensive question that delves into the details of Akebono's weight gain, emphasizing the linear progression of his weight over time. Encourage an analysis of the following aspects:

1. The initial weight of Akebono.
2. The rate at which he gained weight.
3. His weight after a specific duration (8 months).
Prompt respondents to provide insights into the linear equation representing Akebono's weight gain and its implications for predicting his weight at different time points. Facilitate a discussion on the mathematical modeling of weight gain scenarios and the factors influencing the rate of change in weight over time.

Answer 1

A sumo wrestler named Akebono started at 90 kg and gained weight consistently to reach 138 kg after 8 months. The rate of weight gain can be calculated and represented by a linear equation, useful for predicting his future weight.

Step-by-step explanation:

Akebono, a young sumo wrestler, began a high-calorie diet with an initial weight of 90 kg. After 8 months on the diet, his weight increased to 138 kg, showing a consistent linear trend. We are interested in understanding Akebono's rate of weight gain, which is the slope of the line that represents his weight increase over time. This inquiry also focuses on formulating the linear equation that can be used to predict Akebono's weight at various points in time, highlighting the concept of mathematical modeling in weight gain scenarios.

The linear equation for Akebono's weight gain can be written in the form W(t) = mt + b, where W(t) is the weight at time t, m is the rate of weight gain per month, and b is the initial weight. To find the rate, we can use the data points provided: (0, 90) representing his initial weight, and (8, 138) representing his weight after 8 months. The rate of weight gain (m) is the change in weight divided by the time period, thus (138 kg - 90 kg) / (8 months - 0 months).

The importance of understanding this linear progression not only allows us to predict future weight but also gives insight into the effects of diet and exercise on weight over time. Mathematical models like these can demonstrate how factors such as calorie intake and metabolic rate affect the rate of change in weight.