A bottle of lemonade initially has a temperature of 72°F. It is left to cool in a refrigerator that has a temperature of 42°F. After 10 minutes the temperature of the lemonade is 62°F. a. Use Newton's Law of Cooling, T= C+ (To-C) e™, to find a model for the temperature of the lemonade, T, after t minutes. C+ (To -C)e T = T = 42 + (30)e Solve for k and enter the answer (Round to four decimal places.) b. What is the temperature of the lemonade after 15 minutes? T=D°F (Type an integer. Round to nearest degree.) c. When will the temperature of the lemonade be 50°F? t = minutes (Type an integer. Round to nearest minute.)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.