Shinichi Kudo discovered a dead body in a room at midnight with a temperature of 20oC. Since the guest house where the room was located is far from the town, Inspector Megure arrived one hour, 34 minutes and 28 seconds later, and the temperature of the dead body dropped to 18oC. Shinichi noticed that the room temperature is kept constant at 16oC. By recalling some differential equations he learned from the Professor, he was able to estimate the time of death of the corpse. When did the victim died? Express your answer in HH:MM format.

The doubling period of a bacterial population is 1010 minutes. At time t=90t=90 minutes, the bacterial population was 70000.What was the initial population at time t=0?   What is the size of the bacterial population after 4 hours?

please show work

Initially 87 grams of radioactive substance was present. After 4 hours the mass had decreased by 9%. If the rate of decay is proportional to the amount of the substance present at a time . Find the amount remaining after 15 hours   Round your answer to 2 decimal places.

Near the surface of the earth, a ball (with p = 0.1) is released from rest and its flight through the air offers resistance that is proportional to its velocity. How long will it take the ball to reach one-half of its terminal velocity? How far will it travel during this time?

Right now, five hundred fifty pastry chefs have gathered for a tournament in your hometown, and the number is expected to decrease by 15 percent every hour. The organizers want to predict when there will be 50 pastry chefs at the event. Let h(t) = 550(0.85)' represent the number of pastry chefs at the tournament, where t is the number of hours from now. In order to answer the question, let's solve the equation: 50 = 550(0.85)ʻ 1. First, perform one operation to both sides of the equation so that (0.85)' is alone on the right-hand side. Write your resulting equation below. [Do not use your calculator at any point.] Equation: 2. Now, apply the natural logarithm to both sides and simplify the right-hand side by using the property In (m') = bln(m). Write the resulting equation below. [Do not use your calculator at any point.] Equation: 3. Finally, isolate the variable t. Answer: t = hours