Dead Grandmother Syndrome Biology professor Mike Adams has found an increase over the years in the number of students claiming just before an exam that a relative (usually a grandmother) has died. Based on his data, he found that the average number of family deaths per 100 students could be approximated by f(1) = 5.4572 x 10-5°102923x10 where t is the year. Find the average number of deaths per 100 students in 2015 and the rate that the function was increasing in that year. Source: Annals of Improbable Research.

why would one need to use the instantaneous rate of change instead of the average rate of change

If the temperature remains constant, the pressure of an enclosed gas is in- versely proportional to the volume. The pressure of a certain gas within a spherical balloon of radius 9 inches is 20 lb/in?. If the radius of the balloon in- creases to 12 inches, approximate the new pressure of the gas. Sketch a graph of the relationship between the pressure and the volume.

A tsunami (sometimes inaccurately called a “tidal wave”) is a fast moving ocean wave caused by an underwater earthquake. The water first goes down from its normal level to its lowest level, then rises to its highest level above normal. The time it takes to go from lowest level to highest level, and back to lowest level is 15 minutes. The tidal wave continues this pattern until it crashes onto shore. Suppose a tsunami with amplitude of10 meters approaches Honolulu, HI where the normal depth of water is 9meters. Assume the tsunami varies in depth of water sinusoidally with time as it approaches the pier. a) Sketch the graph of the water depths from 0 to 15 minutes.b) Find a particular equation expressing water depth as a function of time. c) What does a negative water depth mean (keeping in mind that there can’t be less than zero water)?

The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the triangle is increasing at a rate of 3 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 10.5 centimeters and the area is 87 square centimeters? cm/min

This scale of earthquake intensity ranges from 1-12?

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

You use a garden hose to fill a wading pool. If the water level rises 11 centimeters every 6 minutes and you record the data point of (18,y). At what rate did the water level change?