The plot in the TB-plane shows the brewing time, B, defined as the time it takes for a tea packet to reach a caffeine concentration of 100 milligrams per liter with water at a temperature of T degrees Celsius. Which of the following equations best models the relationship between B and T ? Choose 1 answer: (A) B=9*0.66^(T) (B) B=9*0.96^(T) (C) B=25*0.66^(T) (D) B=25*0.96^(T)

Question

The plot in the  TB-plane shows the brewing time,  B, defined as the time it takes for a tea packet to reach a caffeine concentration of 100 milligrams per liter with water at a temperature of  T degrees Celsius. Which of the following equations best models the relationship between  B and  T ? Choose 1 answer: (A)  B=9*0.66^(T) (B)  B=9*0.96^(T) (C)  B=25*0.66^(T) (D)  B=25*0.96^(T)

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Identify Given Information: Identify the given information and what is being asked. The problem provides a scenario where the brewing time B is related to the temperature T, and we are asked to choose the equation that best models this relationship. There is no specific data given to calculate the exact relationship, so we must rely on the provided options to determine the most likely correct model.Analyze Equation Structure: Analyze the structure of the given equations. All options are of the form B = constant * rate^(T), where the constant represents the initial brewing time at 0 degrees Celsius, and the rate represents the change in brewing time with each degree change in temperature. We need to determine the most reasonable initial brewing time and the rate at which the brewing time changes with temperature.Consider Realistic Context: Consider the realistic context of the problem. In a realistic scenario, as the temperature increases, the brewing time should decrease because higher temperatures typically speed up the brewing process. This means we are looking for a rate that is less than 1, as a rate greater than 1 would imply that brewing time increases with temperature, which is not typical for brewing tea.Eliminate Options with Rate > 1: Eliminate the options with a rate greater than 1. Looking at the options, we can eliminate any option where the rate is greater than 1, as this would not make sense in the context of brewing tea. However, all given rates (0.66 and 0.96) are less than 1, so we cannot eliminate any options based on this criterion alone.Consider Initial Brewing Time: Consider the initial brewing time constant. The initial brewing time constant (the value multiplied by the rate) should be a reasonable estimate for the brewing time at 0 degrees Celsius. While we do not have specific data, we can consider that a brewing time of 25 minutes at 0 degrees Celsius (option C and D) seems excessively long for tea brewing, even at such a low temperature. Therefore, an initial brewing time of 9 minutes (options A and B) seems more reasonable.Choose Appropriate Rate: Choose the option with the most appropriate rate of decrease. Between the remaining options (A and B), we need to decide between a rate of 0.66 and 0.96. A rate of 0.96 would imply a very slow decrease in brewing time with increasing temperature, which is not very realistic for the brewing process. A rate of 0.66 suggests a faster decrease in brewing time with increasing temperature, which is more consistent with the expected behavior of the brewing process.Select Final Answer: Select the final answer. Based on the analysis, the best model for the relationship between brewing time B and temperature T is the one with a reasonable initial brewing time and a rate that reflects a faster decrease in brewing time with increasing temperature. Therefore, the correct answer is (A) B=9*0.66^(T).

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