4.1 MCQ

The cost, in dollars, to paint x square feet of a house is modeled by the differentiable function C (x). Which of the following is the best interpretation of the statement C'(300)=6 ?

• The cost of painting 6 square feet is $300.

• The cost of painting 300 square feet is $6.

• The cost of painting 300 square feet is $6 per square foot.

• When 300 square feet have been painted, the cost to paint the next square foot is approximately $6.

The functionP(t)models the population of the world, in billions of people, wheretis the number of years since January 1, 2010. Which of the following is the best interpretation of the statementP'(1) = 0.076?

• On February 1, 2010, the population of the world was increasing at a rate of 0.076 billion people per year.

• On January 1, 2011, the population of the world was increasing at a rate of 0.076 billion people per year.

• On January 1, 2011, the population of the world was 0.076 billion people.

• From January 1, 2010 to January 1, 2011, the population of the world was increasing at an average rate of 0.076 billion people per year.

• When the population of the world was 1 billion people, the population of the world was increasing at a rate of 0.076 billion people per year.

A tire that is leaking air has an initial air pressure of 30 pounds per square inch (psi). The functiont=f(p) models the amount of timet, in hours, it takes for the air pressure of the tire to reachppsi. What are the units forf'(p) ?

• hours

• psi

• psi per hour

• hours per psi

On a certain day, the total number of pieces of candy produced by a factory since it opened is modeled by C, a differentiable function of the number of hours since the factory opened. Which of the following is the best interpretation of C'(3) = 500 ?

• The factory produces 500 pieces of candy during its 3rd hour of operation.

• The factory produces 500 pieces of candy in the first 3 hours after it opens.

• The factory is producing candy at a rate of 500 pieces per hour, 3 hours after it opens.

• The rate at which the factory is producing candy is increasing at a rate of 500 pieces per hour per hour, 3 hours after it opens.

For a car driven 100 kilometers at a constant speed, the amount of fuel used as a function of the speed is modeled by a differentiable function . Fuel is measured in liters, and speed is measured in kilometers per hour ( ). In this context, which of the following is a correct interpretation of the statement F'(50)>F'(80)?

• Driving at 50 uses more fuel than driving at 80.

• The rate at which 50 liters of fuel is used is greater than the rate at which 80 liters of fuel is used.

• The rate of change of the speed is greater when driving at 50 than when driving at 80.

• The rate of change of liters of fuel used with respect to the speed is greater when driving at 50 than when driving at 80.

Fort≥ 0 hours,His a differentiable function oftthat gives the temperature, in degrees Celsius, at an Arctic weather station. Which of the following is the best interpretation of H'(24)?

• The change in temperature during the first day

• The change in temperature during the 24th hour

• The average rate at which the temperature changed during the 24th hour

• The rate at which the temperature is changing during the first day

• The rate at which the temperature is changing at the end of the 24th hour

A file is downloaded to a computer at a rate modeled by the differentiable functionf(t), wheretis the time in seconds since the start of the download andf(t)is measured in megabits per second. Which of the following is the best interpretation off'(5)= 2.8 ?

• At time t = 5 seconds, the rate at which the file is downloaded to the computer is 2.8 megabits per second.

• At time t = 5 seconds, the rate at which the file is downloaded to the computer is increasing at a rate of 2.8 megabits per second per second.

• Over the time interval seconds, 2.8 megabits of the file are downloaded to the computer.

• Over the time interval seconds, the average rate at which the file is downloaded to the computer is 2.8 megabits per second.

The height above the ground of a passenger on a Ferris wheel t minutes after the ride begins is modeled by the differentiable functionH, whereH(t) is measured in meters. Which of the following is an interpretation of the statementH'(7.5) = 15.708?

• The Ferris wheel is turning at a rate of 15.708 meters per minute when the passenger is 7.5 meters above the ground.

• The Ferris wheel is turning at a rate of 15.708 meters per minute 7.5 minutes after the ride begins.

• The passenger’s height above the ground is increasing by 15.708 meters per minute when the passenger is 7.5 meters above the ground.

• The passenger’s height above the ground is increasing by 15.708 meters per minute 7.5 minutes after the ride begins.

• The passenger is 15.708 meters above the ground 7.5 minutes after the ride begins.

The rate at which water leaks from a tank, in gallons per hour, is modeled by R, a differentiable function of the number of hours after the leak is discovered. Which of the following is the best interpretation of R'(3)?

• The amount of water, in gallons, that has leaked out of the tank during the first three hours after the leak is discovered

• The amount of change, in gallons per hour, in the rate at which water is leaking during the three hours after the leak is discovered

• The rate at which water leaks from the tank, in gallons per hour, three hours after the leak is discovered

• The rate of change of the rate at which water leaks from the tank, in gallons per hour per hour, three hours after the leak is discovered

The velocity v, in meters per second, of a certain type of wave is given byv(h)= 3 sqaure root of h. What is the rate of change, in meters per second per meter, of the velocity of the wave with respect to the depth of the water, when the depth is 2 meters?

• -3 / 4 sqaure root of 2

• -3 / 8 sqaure root of 2

• 3 / 2 sqaure root of 2

• 3 / sqaure root of 2

• 4 sqaure root of 2