A cup of coffee with cooling constant k = 0.09 min¬' is placed in a room at temperature 20°C. How fast is the coffee cooling (in degrees per minute) when its temperature is T = 85°C? (Give the absolute value of the cooling rate. Use decimal notation. Round your answer up to two decomal places, if necessary.) rate: °C/min Use the Linear Approximation to estimate the change in temperature over the next 6 s when T = 85°C. (Give the absolute value of the temperature change. Use decimal notation. Round your answer up to three decomal places, if necessary.) change:

The deck of a bridge is suspended 285 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by  y = 285 − 16t2. (a) Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 2 and lasting the following amount of time. (i) 0.1 seconds  (ii)0.05 seconds  (iii)0.01 seconds  (b) Estimate the instantaneous velocity (in ft/s) of the pebble after 2 seconds.

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