Question 1

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 .

A) 13.6 cubic inches
B) 23.80 cubic inches
C) 11.57 cubic inches
D) none of the above

none of the above

Accepted Answer

none of the above

Question 2

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

Accepted Answer

A function given by a table of values does not necessarily have a limiting value, as the table may represent discrete data points without implying any behavior as the input approaches a certain value.

Question 3

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.

A) 1088.6 feet per second
B) 1097.5 feet per second
C) 1117.20 feet per second
D) none of the above

1117.20 feet per second

Accepted Answer

1117.20 feet per second

Question 4

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

Accepted Answer

The average rate of change of an increasing function quantifies how much the function's output values increase for a given increase in input values, effectively measuring the function's growth rate over a specific interval.

Question 5

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

Accepted Answer

Functional notation can be used to represent the relationship between the elements in a table of values, especially when the table represents a function, by indicating how each input (usually in one column) is associated with exactly one output (in another column).

Question 6

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

Accepted Answer

When a function is given by a table of values, and there are gaps or missing values, it can be reasonable to estimate these gaps by averaging nearby function values, especially if the function is expected to change smoothly between the known points. This method is a simple form of interpolation.

Question 7

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.

A) 53.25 degrees
B) 57 degrees
C) 40.25 degrees
D) none of the above

Accepted Answer

The average rate of change in temperature is 0.25 degree per chirp per minute. So, if a cricket chirps 53 times per minute, the temperature is approximately 50 + (53 - 40) * 0.25 = 53.25 degrees Fahrenheit.

Question 8

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

Accepted Answer

Limiting values, or limits, are used in calculus to describe the behavior of a function as its input approaches a certain value, including infinity, which helps in understanding the long-term behavior or trends of the function.

Question 9

If   represents the cumulative number of flu cases reported by day &#8203;t, what units are associated with the average rate of change for F with respect to &#8203;t?

Accepted Answer

The answer of If   represents the cumulative number...

Question 10

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.

A) 3.56 million
B) 3.46 million
C) 3.35 million
D) none of the above

Accepted Answer

The average rate of change in population was 0.21 million people per year. So, the population increased by 0.21 million people in 1991 and by another 0.21 million people in 1992. Therefore, the estimated population in 1992 is 3.14 million + 0.21 million + 0.21 million = 3.56 million.

Question 11

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 &#8203;t?

Accepted Answer

The answer of If   represents student enrollment at...

Question 12

The population &#8203;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. &#8203;&#10;A) 16.7 million people&#10;B) 18.66 million people&#10;C) 15.74 million people&#10;D) none of the above

Accepted Answer

The answer of The population &#8203;N of a certain state...

Question 13

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 &#8203;t?

Accepted Answer

The answer of If   represents the total miles...

Deck 2: Functions Given by TableChas