Name:    MAT 121 Section 14: Applied Calculus

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

Simplify the expression.

 A B C D E

2.

Perform the indicated operations and simplify the expression.

 A B C D E

3.

Perform the indicated operations and simplify the expression.

 A B C D E

4.

Simplify the expression.

 A B C D E

5.

Factor the expression.

 A B C D E

6.

Factor out the greatest common factor from the expression.

 A B C D E

7.

Write the equation in the slope-intercept form and then find the slope and -intercept of the corresponding line.

 A B C D

8.

Find an equation of the line that has slope m = 7 and y-intercept b = 1.
 A B C D E

9.

Find an equation of the line that passes through the points (9, 3) and (11, 21).
 A B C D E

10.

Find an equation of the horizontal line that passes through (-6, -1).
 A B C D E

11.

Given the equation 2x + 7y = 4, if x decreases by  4 units, what is the corresponding change in y?
 A B C D E

12.

Find the domain of the function.

 A B C D E

13.

Find the domain of the function.

 A B C D E

14.

Find the domain of the function.

 A B C D E

15.

Find the range of the function.

 A B C D E

16.

The circumference of a circle is given by where r is the radius of the circle. What is the circumference of a circle with a 5-in. radius?
 A B C D E

17.

The management of Titan Tire Company has determined that the weekly demand and supply functions for their Super Titan tires are given by

respectively, where p is measured in dollars and x is measured in thousands of units. Find the equilibrium quantity and price.
 A B C D E

18.

The owner of a luxury motor yacht that sails among the 4,000 Greek islands charges \$500/person/day if exactly 20 people sign up for the cruise. However, if more than 20 people sign up (up to the maximum capacity of 90) for the cruise, then each fare is reduced by \$6 for each additional passenger. Assume at least 20 people sign up for the cruise and let x denote the number of passengers above 20. Find a function R giving the revenue/day realized from the charter.
 A B C D E

19.

A manufacturer has a monthly fixed cost of \$45,000 and a production cost of \$7 for each unit produced. The product sells for \$47/unit. What is the cost function? What is the revenue function? What is the profit function?
 A C(x) = 7x + 45,000, R(x) = 45,000x and P(x) = 40x + 45,000 B C(x) = 7x + 45,000, R(x) = 7x and P(x) = 40x + 45,000 C C(x) = 47x + 7, R(x) = 7x and P(x) = –40x + 45,000 D C(x) = 7x + 45,000, R(x) = 47x and P(x) = 40x - 45,000 E C(x) = 47x + 45,000, R(x) = 45,000x and P(x) = 40x - 45,000

20.

The revenue (in dollars) realized by Apollo from the sale of its inkjet printers is given by

where x denotes the number of units manufactured each month. What is Apollo's revenue when 1,500 units are produced?
 A \$–525,000 B \$–522,000 C \$1,500 D \$–523,500 E \$–526,500

21.

The number of homes with digital TVs is expected to grow according to the function

where t is measured in years, with t = 0 corresponding to the beginning of 2000, and f(t) is measured in millions of homes. How many homes had digital TVs at the beginning of 2000?
 A 714,800 B 1,551,400 C 1.55 D 0.71 E 714.8

22.

For the supply equation where x is the quantity supplied in units of a thousand and p is the unit price in dollars, determine the price at which the supplier will make 2 units of the commodity available in the market.
 A p = \$88 B p = \$40 C p = \$90 D p = \$4 E p = \$54

23.

For the pair of supply and demand equations

where x represents the quantity demanded in units of a thousand and p the unit price in dollars, find the equilibrium quantity and the equilibrium price.
 A x = 12.5, p = \$152.50 B x = 15.5, p = \$191.50 C x = 15.5, p = \$211.50 D x = 14, p = \$172.00 E x = 1.5, p = \$29.50

24.

Determine all values of x at which the function is discontinuous.

 A - 5 B 0, - 5 C 0, 5 D - 3 E 3

25.

Find the values of x for which the function is continuous.

 A B C D E

26.

Use the definition of derivative to determine the slope of the tangent line to the graph of the given function at any point.

 A B C D

27.

Use the definition of derivative to determine the slope of the tangent line to the graph of the given function at any point.

 A B C D

28.

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line.

 A B C D

29.

Let

Find the equation of the tangent line to the curve at the point .
 A B C D

30.

Let .

Find the average rate of change of y with respect to x in the interval from to , from to , from to , and the (instantaneous) rate of change of y at .
 A B C D

31.

The following graph shows the volume of wood produced in a single-species forest. Here is measured in cubic meters/hectare and t is measured in years. By computing the slopes of the respective tangent lines, estimate the rate at which the wood grown is changing at the beginning of year 10 and at the beginning of year 35.

 A cubic meters/hectare per year in the year 10, cubic meters/hectare per year in the year 35 B cubic meters/hectare per year in the year 10, cubic meters/hectare per year in the year 35 C cubic meters/hectare per year in the year 10, cubic meters/hectare per year in the year 35 D cubic meters/hectare per year in the year 10, cubic meters/hectare per year in the year 35

32.

In the following figure, gives the population of a certain bacteria culture at time t after a portion of bactericide A was introduced into the population at . The graph of g gives the population of a similar bacteria culture at time t after a portion of bactericide B was introduced into the population at .

Which population is decreasing faster at and at ?
 A is decreasing faster at , is decreasing faster at B is decreasing faster at , is decreasing faster at C The populations are decreasing at the same rate at , is decreasing faster at D is decreasing faster at , the populations are decreasing at the same rate at