It is math 307 class and about the differential equation

7. + -/4 points My Notes A newly constructed fish pond contains 1000 liters of water. Unfortunately the pond has been contaminated with 5 kg of a toxic chemical during the construction process. The pond's filtering system removes water from the pond at a rate of 200 liters/minute, removes 20% of the chemical, and returns the same volume of (the now somewhat less contaminated) water to the pond. Write a differential equation for the time (measured in minutes) evolution of: The total mass (in kilograms) of the chemical in the pond: dm = dt The concentration (in kg/liter) of the chemical in the pond: dc dt The concentration (in grams/liter) of the chemical in the pond: dc = dt The concentration (in grams/liter) of the chemical in the pond, but with time measured in hours: dc dt Submit Answer 8. + -/4 points My Notes Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. If we measure temperature in degrees Celsius and time in minutes, the constant of proportionality k equals 0.3. Suppose the ambient temperature TA(t) is equal to a constant 76 degrees Celsius. Write the differential equation that describes the time evolution of the temperature 7 of the object. (a) di dt Suppose the ambient temp TA(t) = 76cos( 2 t) degrees Celsius (time measured in minutes). Write the DE that describes the time evolution of temperature 7 of the object. (b ) If we measure time in hours the differential equation in part (b) changes. What is the new differential equation? C it If we measure time in hours and we also measure temperature in degrees Fahrenheit, the differential equation in part (c) changes even more. What is the new differential equation? (d)