A body whose temperature is 180°C is cooled by immersing in a liquid at 60°C. In one minute, the temperature of the body has fallen to 120° C. The rate at which the body temperature (7) change at time t is given by the equation T- -k(T-60). Calculate the time it take for the temperature of the body to fall to 90°C. dt

After an hour, the population of bacteria with a number of P0 found that their number became 3 / 2P0. If the growth rate is proportional to the number of bacteria (P (t) present at time t, find the time required for the number of bacteria to 3 times.

If a ball is dropped from a height of 2304 feet, then its height in feet above the ground is given by h(t)=−16t2+2304 where t is in seconds. Find the average rate of change of the height of the ball as t varies from 8 to 10 seconds.   The average rate of change of the height of the ball is 704 feet per second.

The population of Mexico in millions is described by the formula P(t) year 2030, the population will be increasing at the rate of i = 67e0.0271, where t is the number of years after 1990. In the million people per year. Round to 2 decimal places.

The relationship between the volume, V, measured in cm³, of a balloon and the internal air pressure, P, measured in grams/cm², is given by PV = 45 000. The volume of a balloon is increasing at a rate of 100 cm³s-1. Find the rate of change of the air pressure inside the balloon when the volume is 4 000 cm³.

When drugs are administered into the bloodstream, the amount of the drug present decreases continuously at a constant rate. The amount of a certain drug, Xanaz, in the bloodstream is modeled by the function, where is the initial dosage, and t is the time (in hours) after the initial dose was given. The following chart shows the relationship between the original dose and how much is sti in the system after so much time. Xanax (3mg) amount still in system after X hours 2.5 1.5 0.5 2 10 12 14 16 18 20 22 24 Number of hours after dose was taken After how many hours will there be approximately 1/2 of the original dose in the body? 3. 2. 1. Amount still in the system in mg's

A television camera at ground level is 2000 ft away form a launching pad of a space rocket that is set to take off vertically. The angle of elevation is given by ? = tan−1( ?2000). Find the rate of change of the angle of elevation after launch when the camera and the rocket are 5000 ft apart