Exam 2: Describing Change: Rates

The figure shows the terminal speed, in meters per second, of a raindrop as a function of the size of the drop measured in terms of its diameter. Estimate the derivative of the speed for a diameter of 2 mm.

The figure shows cattle prices (for choice 600-pound steer calves) from October 1994 through May 1995. Identify the input value where the derivative fail to exist.

For the function given, find

Find the slope of the tangent at

Calculate the average rate of change of the function over the given interval. Round your answer to two decimal places.

When advertising an existing commodity, companies are interested in changes in revenue totals at various levels of advertising. The figure shows the advertising threshold effect for a certain commodity. Determine the input value where the line tangent to the graph is not defined.

Given the statement: In five trading days, the stock price rose $2.90. Choose the sentence that best expresses how rapidly, on average, the quantity has changed over the given interval.

The population in a certain country was 364 thousand in 1930 and 3.5 million in 2005. Calculate the percentage change. Round your answer to one decimal place.

The relation u gives the number of people unemployed in a country t months after the election of a new president. Choose the sentence that best expresses u(t) describing the unemployment situation.

Sketch a slope graph of the function.

The amount of airline fuel consumed by an Airline company each year between 2001 and 2009 can be modeled as billion gallons where t is the number of years since 2001. Calculate the amount of fuel consumed in 2009.

Find the derivative of the given function using the algebraic method.

The future value of a certain savings account with no activity besides compounding of interest is modeled as dollars where t is the number of years since $1600 was invested. Calculate the percentage rate of change of the future value when .

The function B gives the balance, in dollars, in a mutual fund t years after the initial investment. Assume that no deposits or withdrawals are made during the investment period. What is the financial interpretation of .

The function p gives the number of meters from an airport that a plane has flown after t minutes. What are the units on .

The future value of a certain savings account with no activity besides compounding of interest is modeled as dollars where t is the number of years since $1400 was invested. Numerically estimate to the nearest cent the rate of change of the future value when .

Using the following table, estimate

Find the slope of the tangent to the graph of f (x) at any point.

The function f gives the weekly profit, in thousand dollars, that an airline makes on its flights from Boston to Washington D.C. when the ticket price is p dollars. Choose the sentence that best expresses .

The function w gives the number of words per minute (wpm) that a student in a keyboard class can type after t weeks in the course. Is it possible for to be negative? Explain.