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A fitness trainer is analyzing the weight loss progress of his best client over a period of 6 months, to use it as for marketing. He recorded the weight of the client at the beginning and end of each month. Using straight line fitting, he came up with an equation 𝑊=−8𝑡+98W=−8t+98, where W = Weight in Kg, t= time in months.Now you want to check weather this equation is correct or not so you collected the data from the gym, the data is given in table below.                        You were impressed by the performance of the fitness trainer, so you want to get trained under him, you assumed that the rate of weight loss (weight loss per month) will be same as the case of the best client mentioned in the question. Considering your assumption is true, how many days are required for you to loss weight from 100 kg to 72 kg.Note: 1 month has 30 days

Question

A fitness trainer is analyzing the weight loss progress of his best client over a period of 6 months, to use it as for marketing. He recorded the weight of the client at the beginning and end of each month. Using straight line fitting, he came up with an equation 𝑊=−8𝑡+98W=−8t+98, where W = Weight in Kg, t= time in months.Now you want to check weather this equation is correct or not so you collected the data from the gym, the data is given in table below.                        You were impressed by the performance of the fitness trainer, so you want to get trained under him, you assumed that the rate of weight loss (weight loss per month) will be same as the case of the best client mentioned in the question. Considering your assumption is true, how many days are required for you to loss weight from 100 kg to 72 kg.Note: 1 month has 30 days

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Solution

The equation given by the fitness trainer is W = -8t + 98, where W is the weight in kg and t is the time in months. This equation suggests that the client is losing 8 kg per month.

If you want to reduce your weight from 100 kg to 72 kg, you need to lose 28 kg.

Using the rate of weight loss from the equation, which is 8 kg per month, you can calculate the time required to lose 28 kg as follows:

28 kg ÷ 8 kg/month = 3.5 months

Since 1 month is considered to have 30 days, the time in days will be:

3.5 months × 30 days/month = 105 days

So, it will take approximately 105 days for you to reduce your weight from 100 kg to 72 kg, assuming the rate of weight loss is the same as the client in the question.

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