Question 1

The following figure gives both supply and demand curves for a certain product. If the price is $50 per item, how many items will the consumers buy?

Accepted Answer

The answer of The following figure gives both supply and...

Question 2

A premium ice cream company finds that at a price of $5.50, demand for their ice cream cones is 2500. For each $0.25 increase in price, the demand decreases by 50. Graph the revenue function and find the price that will maximize revenue.

Accepted Answer

The answer of A premium ice cream company finds that...

Question 3

The following table gives the number of students taking an applied calculus course at a community college. Find the change in the number of students taking the course between 2001 and 2004.

Accepted Answer

The answer of The following table gives the number of...

Question 4

A textbook company had fixed costs of $15,000 and variable costs of $20 for a certain book. The company sells the books for $40 each. What is the break-even point for the company (to the nearest book)?

Accepted Answer

The answer of A textbook company had fixed costs of...

Question 5

The following graph shows the quantity of goods purchased by consumers at various prices. If the price is $15 per item, how many items do consumers purchase?

Accepted Answer

At the price of $15, the graph intersects with the quantity axis at 8, so consumers purchase 8 items.

Question 6

Suppose that  is the price per unit (in dollars) of widgets which will induce producers to supply q thousand widgets to the market, and suppose that  is the price per unit at which consumers will buy q thousand units. If  and  , what do you predict about the future selling price of widgets (currently at $10)?

Accepted Answer

The fact that the price at which consumers are willing to buy the widgets is higher than the price at which producers are willing to supply them suggests that there is likely to be an excess demand for widgets at the current price level of $10. This excess demand is likely to exert upward pressure on the selling price of widgets in the future, since producers will be able to charge more and still find willing buyers. Therefore, the best choice is A, that the price of widgets will rise.

Question 7

The following figure gives both supply and demand curves for a certain product. If the price is $75 per item, would you expect the market pressures to push the price higher or lower?

Accepted Answer

At a price of $75 per item, the quantity demanded is higher than the quantity supplied, creating a surplus. This means that there is more supply than demand at this price, which puts downward pressure on prices. As a result, the market pressures would push the price lower.

Question 8

Suppose that  is the price per unit (in dollars) of widgets which will induce producers to supply q thousand widgets to the market, and suppose that  is the price per unit at which consumers will buy q thousand units. Which is larger, S(150) or S(100)?

Accepted Answer

The answer of Suppose that  is the price per...

Question 9

A $2000 pump depreciates linearly. It is worth $1200 in 4 years. How many years will it be before the pump is worth nothing?

Accepted Answer

The answer of A $2000 pump depreciates linearly. It is...

Question 10

The number of reported offenses of violent crime in the U.S. between 1983 and 1996 is given in the following table.
A. Find the average rate of change between 1983 and 1992 (to the nearest integer).
B. Find the average rate of change between 1992 and 1996 (to the nearest integer).

Accepted Answer

The answer of The number of reported offenses of violent...

Question 11

Values for g(x) are given in the following table. Does it appear that g(x) is concave up or concave down?

Accepted Answer

The answer of Values for g(x) are given in the...

Question 12

The distance  in feet that a golf ball will fall in t seconds if dropped from a very high tower is given by the formula  . Make and label a table or a graph of values of f(t) giving distances fallen for the time period  . Using your table or graph, the change in the height of the golf ball between times t = 5 and t = 7 is _____ feet, and the average rate of change in the height of the golf ball between times t = 5 and t = 7 is____ feet per second.

Accepted Answer

The answer of The distance  in feet that a...

Question 13

The table gives information about the number of cases of pancreatic cancer diagnosed in the United States.  A) Find the average rate of change in number of cases from 1997 to 2002.
B) Find the average rate of change in number of cases from 2002 to 2004.
C) Is the average rate of change increasing or decreasing?

Accepted Answer

The answer of The table gives information about the number...

Question 14

Consider the following graph. Between point A and point B, the graph is: (mark all that apply)

Accepted Answer

The answer of Consider the following graph. Between point A...

Question 15

A $3000 pump depreciates linearly . It is worth $2200 in 4 years. Find a formula for the value of the pump, V, as a function of time, t (in years) since it was purchased.

Accepted Answer

The answer of A $3000 pump depreciates linearly . It...

Question 16

A textbook company had fixed costs of $15,000 and variable costs of $20 for a certain book. The company sells the books for $30 each. Find a formula for the profit function,  .

Accepted Answer

The answer of A textbook company had fixed costs of...

Question 17

Find the average rate of change of  between t = 1 and t = 3. Round to two decimal places.

Accepted Answer

The answer of Find the average rate of change of...

Question 18

The total sales of household computers in the U.S., as measured by sales to retail consumer dealers, in millions of dollars, was 2,385 in 1984 and 16,585 in 1997.
A. Find the average rate of change in sales between 1984 and 1997 (in millions of dollars, to the nearest tenth).
B. Use your answer to estimate total sales in 2000 (in millions of dollars, to the nearest tenth).

Accepted Answer

The answer of The total sales of household computers in...

Question 19

The following table gives the number of students taking an applied calculus course at a community college.
A. Find the average rate of change in the number of students taking the course between 2000 and 2004 (in students per year).
B. If the average rate of change continues at the same rate as between 2000 and 2004, in which year will the number of students taking the course first exceed 900?

Accepted Answer

The answer of The following table gives the number of...

Question 20

Values of a linear cost function are given in the following table. Find a formula for the cost function.

Accepted Answer

The answer of Values of a linear cost function are...

Quiz 1: Functions and Change