2) A police detective investigating a murder finds the body of the victim at 9:30 pm. At that time, the temperature of the victims body is 65° F. After 45 minutes, the victims body has cooled to 60° F. The surrounding temperature outside has been constant 50°F for the entire day. Assuming that the victim's body follows Newton's law of cooling : i) Write down a differential equation for the temperature of the victims body (your answer will involve a proportionality constant). ii) Find the general solution (your answer will involve a proportionality constant). iii) Use the provided information to determine the temperature as a function of time, for the victim's body. You may take t = 0 to be 9:30 pm. iv) Typical human body temperature is 98.6° F. Use this to estimate the time of death of the victim.

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 differentia…