Exam 2: Functions Given by TableChas

The speed of sound in air depends on the temperature.When the temperature is 32 degrees Fahrenheit, the speed of sound is 1087.5 feet per second.The average rate of change for ​S is 1.1 feet per second per degree Fahrenheit.Use these facts to estimate the speed of sound in air when the temperature is 59 degrees Fahrenheit. ​

The temperature in degrees Fahrenheit can be estimated from the number of cricket chirps per minute.If a cricket chirps 40 times per minute, the temperature is approximately 50 degrees Fahrenheit.The average rate of change in temperature is 0.25 degree per chirp per minute.Use these facts to estimate the temperature when a cricket chirps 53 times per minute. ​

If represents the total miles a car travels in t hours, what units are associated with the average rate of change for M with respect to ​t?

The resident population of Oklahoma in 1990 was 3.14 million.From 1990 to 2000 the average rate of change in population was 0.21 million people per year.Use these facts to estimate the Oklahoma resident population in 1992. ​

If represents student enrollment at your university in year t, what units are associated with the average rate of change for S with respect to ​t?

Every function given by a table of values has a limiting value.

When a function is given by a table of values, it is sometimes reasonable to fill in gaps by averaging nearby function values.

A balloon that originally holds 13.6 cubic inches of air springs a leak.Let represent the volume, in cubic inches, of air in the balloon t minutes after the balloon starts to leak air.The average rate of change of V is -1.02 cubic inches per minute.Use these facts to estimate . ​

The population ​N of a certain state today is 16.7 million people.The average rate of change for N is -0.16 million people per year.Use these facts to estimate the population of the state 6 years from now. ​

If represents the cumulative number of flu cases reported by day ​t, what units are associated with the average rate of change for F with respect to ​t?

Limiting values give information about the long-term behavior of functions.

It is never appropriate to use functional notation when dealing with a table of values.

The average rate of change of an increasing function is a measure of the rate at which the function grows.