(18 points) You're roasting a chicken (or a tofurkey if you prefer.) For food safety reasons,...

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(18 points) You're roasting a chicken (or a tofurkey if you prefer.) For food safety reasons, you need to cook a chicken until the temperature in the center is 165 degrees F (74 C). Your recipe says to set the oven to a temperature of 400 degrees F (205 C). The cold chicken measures 35 degrees F. After 15 minutes, the meat thermometer inserted into the center reads 85 degrees F. For this problem, you can solve it in Fahrenheit or Celsius, depending on which you're more comfortable with. a. Set up a differential equation and two conditions to model this situation. b. Solve the differential equation, including the information from the initial conditions, to find a function of the temperature in terms of the time in minutes. Show the steps of your solution. c. After how many minutes should you take the chicken out of the oven? d. Create a graph that represents the internal temperature of the chicken over time. e. You got too distracted trying to solve the equation instead of watching your food! Find lim T(t) and explain what this means in terms of your chicken. 1-0 (18 points) You're roasting a chicken (or a tofurkey if you prefer.) For food safety reasons, you need to cook a chicken until the temperature in the center is 165 degrees F (74 C). Your recipe says to set the oven to a temperature of 400 degrees F (205 C). The cold chicken measures 35 degrees F. After 15 minutes, the meat thermometer inserted into the center reads 85 degrees F. For this problem, you can solve it in Fahrenheit or Celsius, depending on which you're more comfortable with. a. Set up a differential equation and two conditions to model this situation. b. Solve the differential equation, including the information from the initial conditions, to find a function of the temperature in terms of the time in minutes. Show the steps of your solution. c. After how many minutes should you take the chicken out of the oven? d. Create a graph that represents the internal temperature of the chicken over time. e. You got too distracted trying to solve the equation instead of watching your food! Find lim T(t) and explain what this means in terms of your chicken. 1-0