Saul the college calculus student wants to reheat some soup between study sessions. Saul puts the bowl in the microwave straight from the refrigerator. When the soup has been heating up for t minutes, its temperature is given by r(t) = 2t4 +37 where r(t) is measured in degrees Fahrenheit. We will use calculus to study how fast the soup heats up. a) (2 points) What was the temperature of the soup when Saul took it out of the refrigerator? (Include units.) Temperature: b) (2 points) Saul wants the soup to be 199. How long should he microwave the soup to hit this temperature? (Include units.) Time: c) (4 points) Find the average rate of change of the temperature of the soup during the first two minutes. (Include units.) Average rate of change: d) (4 points) Find the average rate of change of the temperature of the soup during the time interval [1,2]. (Include units.) Average rate of change: e) (4 points) Let An denote the average rate of change of the temperature during the time interval [2, 2+ h] if h > 0, and the average rate of change of the temperature during the time interval [2 + h, 2] if h < 0. Find an expression for A. SIMPLIFY your result. f) (3 points) Evaluate the limit lim A. (Include units). h0 An lim Ah h0 = = g) (3 points) Explain what the value found in the previous part means in the context of the problem. (Don't forget units.) h) (2 points) The soup bowl might crack if its temperature ever changes at a rate faster than 50/min. Is the bowl in danger of cracking at time t = 2? Explain.