The graph below shows T(x), the temperature of a bowl of soup as a function of...

 

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The graph below shows T(x), the temperature of a bowl of soup as a function of the time it has been sitting on the counter to cool. a) Find the average rate of change in temperature with respect to time during the first 25 minutes. Include appropriate units in your answer. b) Find the average rate of change in temperature with respect to time between x = 25 and x = 40. Temperature of soup (C) 100 90 80 70 60 50 10 30 20 10 0 0 (0,95) (25,65.75) 10 20 30 Minutes on counter (50,36.5) 40 (40,48.2) b) Write a complete sentence that interprets the meaning of the number 10 in this context. c) Are the answers to parts a and b the same or different? Explain why this makes sense in terms of the shape of the graph. 50 2. A large koi pond is filled from a garden hose and can be modeled by the function V(t) = 300 + 10t where V is the volume of water in the pond (in gallons) after t minutes. Write a complete sentence that interprets the meaning of the number 300 in this context. 60 The graph below shows T(x), the temperature of a bowl of soup as a function of the time it has been sitting on the counter to cool. a) Find the average rate of change in temperature with respect to time during the first 25 minutes. Include appropriate units in your answer. b) Find the average rate of change in temperature with respect to time between x = 25 and x = 40. Temperature of soup (C) 100 90 80 70 60 50 10 30 20 10 0 0 (0,95) (25,65.75) 10 20 30 Minutes on counter (50,36.5) 40 (40,48.2) b) Write a complete sentence that interprets the meaning of the number 10 in this context. c) Are the answers to parts a and b the same or different? Explain why this makes sense in terms of the shape of the graph. 50 2. A large koi pond is filled from a garden hose and can be modeled by the function V(t) = 300 + 10t where V is the volume of water in the pond (in gallons) after t minutes. Write a complete sentence that interprets the meaning of the number 300 in this context. 60

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a The average rate of change in temperature during the first 25 minutes can be found by calculating ... View the full answer