Exponential, Trigonometric, and Variables

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Find the sale price when the original price is $37.00 and the discount rate is 44%.
a.
$20.72
c.
$35.37
b.
$16.28
d.
$1.63
a.
$20.72
How are exponential functions characterized? Exponential functions are characterized by the fact that:
a.
the graph will always be positive
c.
their growth rate is less than their value
b.
their growth rate is proportional to their value
d.
the value is greater than the growth rate
b.
their growth rate is proportional to their value
After receiving a discount of 6.5% on its bulk order of notebooks, John's Office Supply pays $6732. What was the price of the order before the discount?
a.
$6631
c.
$7200
b.
$7170
d.
$6294
c.
$7200
Jack is currently driving into a headwind (17% decrease). If his normal mileage is 41 mpg, what will his car's mileage be in the headwind? Round your answer to the tenths place.
a.
41 mpg
c.
7.3 mpg
b.
34 mpg
d.
58 mpg
b.
34 mpg
Given the following table, determine the missing value.
Growth Factor
1.01
1.45
4.61
1.30
Percent
1%
45%
361%
?
a.
130%
c.
70%
b.
30%
d.
13%
b.
30%
Brand X copier has improved its copier so that it produces 10% more copies than its old model. If the old model ran 420 copies per hour, how many copies would the new model run? Round your answer to the nearest whole number.
a.
221 copies per hour
c.
462 copies per hour
b.
435 copies per hour
d.
447 copies per hour
c.
462 copies per hour
The normal gasoline mileage of a car is 48 mpg. On a smooth road, the cars mileage is 12% higher. What is its mileage on a smooth road? Round your answer to the tenths place.
a.
53.8 mpg
c.
50.1 mpg
b.
48.2 mpg
d.
58.5 mpg
a.
53.8 mpg
Given the following table, determine the missing value.
Growth Factor
1.08
1.12
3.22
1.51
Percent
8%
12%
?
51%
a.
222%
c.
22%
b.
322%
d.
22.1%
a.
222%
The sales tax in the city of Strawberry is 10.5%. What is the growth factor for any item purchased at your local Circle mart?
a.
10.5
c.
105
b.
1.105
d.
1.05
b.
1.105
In exponential growth and decay problems, what is the independent variable?
The independent variable is almost always:
a. f= function
b. e = exponent
c. t = time
d. A = amount in the model
c. t = time
The Shop and Save is starting their annual clearance and the store has sent out to all their customers a coupon book offering a variety of savings on their products. The LCD television that you have wanted was reduced by 35% prior to the annual clearance. In addition, the coupon book has a 10% off coupon for the LCD television. Determine what you would pay after applying the discounts given that the price of the LCD television was $1,325. Round your answer to the nearest cent.
a.
$728.75
c.
$596.25
b.
$775.13
d.
$46.38
b.
$775.13
Your local bike shop is having a sale. The shop needs to make room for the 2009 models and all 2008 models are on sale. The shop has a store wide sale and has reduced all 2008 models by 23%. In addition, you found a flier for the shop offering an additional 12% off the 2008 Bianchi, Via Nirone. Determine the decay factor corresponding to each percent decrease.
a.
23; 12
c.
77; 88
b.
0.23; 0.12
d.
0.77; 0.88
d.
0.77; 0.88
What is the decay factor that corresponds to a 10% decrease?
a.
10
c.
90
b.
0.10
d.
0.90
d.
0.90
What is the decay factor that corresponds to a 35% decrease?
a.
0.35
c.
0.65
b.
35
d.
65
c.
0.65
Your local dry cleaners is running a special. The dry cleaner is offering a 13% discount for any drop off that is over $40. Also, they are running a neighborhood special of an additional 5% off. Given this information, determine the decay factor corresponding to each percent decrease.
a.
34.8; 33.06
c.
0.87; 0.95
b.
0.384; 0.3306
d.
87; 95
c.
0.87; 0.95
Suppose that you are given that the sale price of an item is $54.32. This was after applying a store wide 10% discount and then a coupon discounting the item by 5%. Given this information, determine the original price of the sale item. Round your answer to the nearest cent.
a.
$60.36
c.
$63.53
b.
$57.18
d.
$59.32
c.
$63.53
Your local Ford dealership is having a sale. All 2008 model trucks have been reduced by 15% and for a limited time, all trade-ins will discount the truck an additional 5%. Given this information, determine the decay factor corresponding to each percent decrease.
a.
0.85; 0.95
c.
15; 5
b.
85; 95
d.
0.15; 0.05
a.
0.85; 0.95
What is the decay factor that corresponds to a 99% decrease?
a.
99
c.
1
b.
0.99
d.
0.01
d.
0.01
Today's newspaper contains a 20%-off coupon at Old Army. The $100 jacket that you want was already reduced by 40%. What as the final price that you paid for the jacket?
a.
$48
c.
$42
b.
$46
d.
$40
a.
$48
A $300 suit is on sale for 30% off. In addition to the sale, you have a 20% coupon that you found in your local paper. Determine the price that you will pay after the discounts. Round your answer to the nearest cent.
a.
$150.00
c.
$168.00
b.
$240.00
d.
$210.00
c.
$168.00
The price for a gallon of whole milk has increased from 2006 to 2008. From 2006 to 2007, the cost of whole milk increased by approximately 56%. From 2007 to 2008, the cost of milk whole milk increased by approximately 42%. If, on average, the cost for a gallon of whole milk nationwide was $1.99 at the beginning of 2006, determine the cost for a gallon of whole milk by the end of the year 2008. Round your answer to the nearest cent.
a.
$3.10
c.
$2.83
b.
$4.41
d.
$3.94
b.
$4.41
How do exponential functions differ from regular functions? In exponential functions the variable is:
a.
always negative
c.
representing the power
b.
representing the base
d.
always t
c.
representing the power
Great Mountain Ride shop has seen an increase in the number of people that have purchased a new snow board over the last three days. In order to keep up with demand, the manager of the shop has recorded the number of people that have purchased a snow board over a five day period. His data was given in the following table:

Day 1
Day 2
Day 3
Day 4
Day 5
% increase of the number of people who bought snow boards
10%
15%
5%
8%
12%

Given that the total number of people that purchased a snowboard on day 5 was 250 people, determine how many people purchased snowboards the day before the manager started to collect her data. Round your answer to the nearest person.
a.
155 people
c.
160 people
b.
156 people
d.
161 people
b.
156 people
What happens to a graph that is representative of exponential decay? The graph goes:
a.
down and to the right
c.
up and to the right
b.
down and to the left
d.
up and to the left
a.
down and to the right
What is the growth factor that corresponds to a product that increases its value first by 2%, and then increases by 5% of its value, and finally increases by 12% of its value? Round to the tenths place.
a.
1.20
c.
1.19
b.
3.19
d.
1
...
You are planning on purchasing a new car and have your eye on a specific model. You know that new car prices are projected to increase at a rate of 5% per year for the next few years.

Find the cost of the car 3 years from now if the current price is $26,000. Write the equation that represents the projected cost C and provide a solution for the problem.
a.
$81,900
c.
$82,404.45
b.
$30,098.25
d.
$74,285.71
a.
$81,900
You are planning on purchasing a new car and have your eye on a specific model. You know that new car prices are projected to increase at a rate of 5% per year for the next few years.

Find the cost of the car 4 years from now if the current price is $27,000. Write the equation that represents the projected cost C and provide a solution for the problem.
a.
$115,751.53
c.
$106,666.67
b.
$32,818.67
d.
$113,400
b.
$32,818.67
Sam just purchased a new car. After his employee discount and the sale that the dealership applied to the original price, Sam paid $13,734.60. If Sam's employee discount was applied to the original price after the dealer discount, then determine the original price of the vehicle given that the employee discount was 8% and the dealership discount was 25%. Round your answer to the nearest cent.

a.
$20,375.21
c.
$19,250.13
b.
$18,350.33
d.
$19,905.22
d.
$19,905.22
It's winter and the powder on Vail Mountain has never been better. You decide to measure the snowfall over a three hour period to determine the amount of snow that has fallen. The first hour you record a 5% increase in snowfall, the second hour you record a 8% increase in snowfall, and the third hour you record a 11% increase in snow fall. Over the three hour period, the snow has increased to a height of 17 inches. How high was the snow on the first hour just before it started to snow? Round your answers to the nearest tenth of an inch.
a.
13.3 inches
c.
13.7 inches
b.
13 inches
d.
13.5 inches
d.
13.5 inches
You recently purchased a new snowboard for the upcoming winter. The board, with bindings, came out to be $315.32. You were told that the store was running a sale on the make and model of snowboard that you purchased and, because you were a member of the shop, you received an additional discount. If the store discount on the make and model of board that you purchased is 15% and the shop member discount is 5%, then determine the original price of the item. Round your answer to the nearest cent.
a.
$368.02
c.
$299.55
b.
$390.49
d.
$175.18
b.
$390.49
Determine the amplitude or period as requested.
Amplitude of y=-1/5sinx
b. 1/5
Convert the angle to radians. Leave as a multiple of pi.
-90 degree
c. -pi/2
Consider the following sine regression model
Predict y(14).
a.
94.8
b.
61.5
c.
9.4
d.
77.3
b.
61.5
Find cos-10.9455 to the nearest degree
a.
26°
c.
19°
b.
71°
d.
41°
c.
19°
A surveyor is standing 550 feet from the base of a redwood tree in the California Redwood Forest. The tree is 362 feet tall. Sketch a drawing that models the situation and then find the angle of elevation of the top of the tree from the spot where the surveyor is standing.
a.
48.8o
b.
33.4o
c.
56.6o
d.
41.0o
b.
33.4o
What is the ratio of the wavelengths of these two notes?
a.
3 to 2
b.
2 to 3
c.
4 to 3
d.
5 to 6
c.
4 to 3
What is the range of a cosine function?
a.
irrational numbers
c.
positive numbers
b.
negative numbers
d.
All real numbers between -1 and 1 including -1 and 1
d.
All real numbers between -1 and 1 including -1 and 1
The average number of customers per day at a home improvement store is given in the following table. Let x represent the day where 1 = Sun of the first week, 7 = Sat of the first week, 8 = Sun of the second week, and 14 = Sat of the second week. Use a graphing calculator to produce a sine regression model for the data. Round a, b, c, and d to the nearest thousandth.

a.
33.690sin(0.887x + 1.337) + 81.684
b.
34.081sin(0.888x - 1.341) + 82.822
c.
34.081sin(0.888x + 1.341) + 82.822
d.
33.690sin(0.887x + 1.337) - 81.684
c.
34.081sin(0.888x + 1.341) + 82.822
A small plane is 4 miles by land away from the airport. The angle of elevation from the airport to the airplane is 4072-06-02-01-00_files/i0160001.jpg? What is the altitude of the plane? Round your answer to the nearest tenth of a mile.

a.
0.1 mile
c.
35.1 miles
b.
0.5 mile
d.
8.6 miles
b.
0.5 mile
Which function is illustrated by the following graph?

a.
cosine function
c.
Tangent function
b.
Sine function
d.
Cotangent function
a.
cosine function
Period of y= -1/3sin2x

a.
-1/3
b.
pi/3
c.
1/3
d.
pi
d. pi
Which of the following statements is true?
a.
sin 18° = cos 72°
b.
sin 55° = cos 55°
c.
sin 72° = cos 18°
d.
Both a and c.
d.
Both a and c.
Evaluate the function requested. Write your answer as a fraction in lowest terms.
Find sin A.
a. sin A = 4/3
b. sin A = 4/5
c. sin A = 3/5
d. sin A = 5/4
b. sin A = 4/5
The cosine of the complimentary angle to 58°
a.
0.74
c.
0.83
b.
0.85
d.
0.94
b.
0.85
f(x)= -2 sin(x)

a.
Graph A
b.
Graph B
c.
Graph C
d.
Graph D
d.
Graph D
If y varies directly as x and y = 208 when x = 16, what is the value of y when x = 11?
a.
143
b.
121
c.
16
d.
169
a.
143
For the function defined by f(x)= 12/x^2
What is the constant of proportionality?
a.
120
c.
12
b.
undefined
d.
1200
c.
12
The variables x and y vary directly. Use the given values to write an equation that relates
x and y.

x = 18
y = 6
y=1/3 x
Explain why no part of the graph y=10/x^2 appears below the x-axis?
a.
The y-value is always negative
c.
The y-value is always zero
b.
The y-value is always positive
d.
The y-value is always 10
b.
The y-value is always positive
10/x=2

a.
x = 5
c.
x = 20
b.
x = 10
d.
x = 15
a.
x = 5
There are about 100 calories in 30 grams of Swiss cheese. Ruth ate 70 grams of this cheese. About how many calories were in the cheese that she ate if the number of calories varies directly as the weight of the cheese?
a.
224
c.
218
b.
280
d.
233
d.
233
A project can be completed by 5 workers in 24 days. How many workers are needed to finish the project in 15 days? The time to complete a project is inversely proportional to number of people who are doing the project.
a.
10
c.
6
b.
12
d.
8
d.
8
i=120/d^2
What is the constant of proportionality?
a.
120
c.
12
b.
undefined
d.
1200
a.
120
The distance D that a spring is stretched by a hanging object varies directly as the weight W of the object. If a 9-kg object stretches a spring 54 cm, find the distance when the weight is 2-kg. Round your answer to the nearest whole centimeter.
a.
65 cm
b.
12 cm
c.
0 cm
d.
6 cm
b.
12 cm
Suppose y varies directly as x. If y = 7 when x = 28, what is the value of x when y = 3?
a.
7
b.
9
c.
12
d.
16
c.
12
The number of hours, h, it takes for a block of ice to melt varies inversely as the temperature, t. If it takes 3 hours for a square inch of ice to melt at 60 degrees, find the constant of proportionality
a.
150
c.
210
b.
180
d.
200
b.
180
The distance an object falls when dropped from a tower varies directly as the square of the time it falls. If the object falls 144 feet in 3 seconds, how far will it fall in 18 seconds?
a.
4536 ft
b.
5832 ft
c.
5184 ft
d.
288 ft
c.
5184 ft
If y varies directly as x and y = 20 when x = 6, what is the value of y when x = 24?
a.
36
b.
80
c.
30
d.
4
b.
80
The perpendicular sides of a triangular rug measure 6 feet and 9 feet. Calculate the area of the rug.
a.
39 sq. ft
c.
21 sq. ft
b.
27 sq. ft
d.
19 sq. ft
b.
27 sq. ft
Robert wants to start an IRA that will have $550,000 in it when he retires in 25 years. How much should he invest quarterly in his IRA to do this if the interest is 6% compounded quarterly? Assume an Annuity Due. Round to the nearest cent.
a.
$2,368.29
c.
$2,403.81
b.
$2,378.30
d.
$2,408.91
a.
$2,368.29
Find Tan A for the triangle below
a.
2.5
b.
0.4
c.
2.67
d.
0.375
a.
2.5
Rectangle topped by a semi circle
a.
35.57 m
b.
65.40 m
c.
59.70 m
d.
49.70 m
d.
49.70 m
The diameter of the moon is 2155 miles. Find volume of the moon. Leave pi in your answer.
a.
Volume: 133*x^10 pi
c.
Volume: 18,576,100
b.
Volume: 4,644,025
d.
Volume: 1,667,978,979
d.
Volume: 1,667,978,979
The phases of the moon are periodic and repetitive. A new moon occurs when no moon is visible to an observer on Earth. During the first quarter, half of the side of the moon facing the Earth is visible. During a full moon the entire side of the moon is visible. During the last quarter the other half of the side of the moon facing Earth is visible.

The U.S. Naval Observatory lists the following dates for phases of the Moon in the year 2008.
Using the information above, plot the data points and produce a sine regression model for the data. Round a, b, c, and d to the nearest 0.001. Then use your model to predict how much of the moon will be visible 1 full year later, provided the sky is clear and assuming the year has 365 days. Give your answer as a percent.
a.
11% of the moon will be visible
b.
42% of the moon will be visible
c.
0% of the moon will be visible
d.
73% of the moon will be visible
d.
73% of the moon will be visible
Mrs. Matthews wants to have $18,000 in the bank in 2 years. If she deposits $9000 today at 6% compounded quarterly for 2 years, how much additional money will she need to reach the desired $18,000?
a.
$10,138.43
c.
$8864.49
b.
$7861.57
d.
$0
b.
$7861.57
The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from the center of the earth. If a person weighs 180 pounds on the surface of the earth and the radius of the earth is 3900 miles, what will the person weigh if he or she is 850 miles above the earth's surface? Round your answer to the nearest hundredth of a pound.
a.
121.34 lb
b.
121.74 lb
c.
122.74 lb
d.
120.84 lb
a.
121.34 lb
A 50-year-old male purchased a 20-Year Endowment insurance policy at the age of 40.The face value of the policy was $85,000. He asks his insurance agent for a reduced paid up insurance nonforfeiture option. Given the table below and the permanent insurance amount of $48.20 per thousand, determine the reduced paid up insurance value and the annual premium.

a.
Annual Premium of $4,097.00; Reduced Paid Up option of $47,770
c.
Annual Premium of $4,625.00; Reduced Paid Up option of $70,890
b.
Annual Premium of $4,500.00; Reduced Paid Up option of $35,785
d.
Annual Premium of $4,821.00; Reduced Paid Up option of $85,000
a.
Annual Premium of $4,097.00; Reduced Paid Up option of $47,770
Below is a graph of exponential functions labelled I through VI.
Determine which of the following exponential formula(s) represents exponential function II in the graph above.
a. x
You invest $4000 in a bank account with 5% interest compounded annually. You are wondering how long it would take for your money to double.

What equation will you use to solve the problem and how long will it take for your money to double?
a. 14.2 years
b. 2 years
c. 7 years
d. 28 years
a. 14.2 years
You have just graduated from college and purchased a car for $8000. Your credit limit is $20,000. Assume that you make no payments and purchase nothing more and that there are no other fees. The monthly interest rate is 12%. Find the y-intercept for the exponential function which represents how much you will owe (represented by y) after x months with no more purchases or payments.
a.
(0, 20,000)
c.
(0, 8000)
b.
(8000, 0)
d.
(20,000, 0)
c.
(0, 8000)
You have decided to purchase a car for $22,346.16. The credit union requires a 10% down payment and will finance the balance with a 5.4% annual interest loan for 36 months. The sales tax in your city is 7.6%, and the license and title charges are $125.13. Determine the amount that the credit union will finance you for. Round your answer to the nearest cent.
a.
$24,179.10
c.
$21,761.20
b.
$24,169.60
d.
$21,752.64
d.
$21,752.64
What is the period for the graph of y = sin 0
(Sketch a graph to help determine the answer.)
a.
180
c.
90
b.
270
d.
360
d.
360
In a sale, the price of a computer is reduced from $1,280 to $1,030. Find the rate of the discount and the amount of the discount. Round the discount rate to the nearest tenth of a percent if necessary.
a.
18.8%; $240
c.
19.5%; $250
b.
24.3%; $250
d.
23.3%; $240
c.
19.5%; $250
Use the diagram of the right triangle above and round your answer to the nearest hundredth.
If m < a = 30 degree
and b = 12 meters, find a.
a.
17.32 m
c.
14 m
b.
6.93 m
d.
9.99 m
b.
6.93 m
Your current CD matures in a few days. You would like to find an investment with a higher rate of return than the CD. Stocks historically have a rate of return between 10% and 12%, but you do not like the risk involved. You have been looking at bond listings in the newspaper. A friend wants you to look at the following corporate bonds as a possible investment.
If you buy three of the ABC bonds with $10 commission for each, how much will it cost?
a.
$3142.50
b.
$1047.50
c.
$3172.50
d.
$1077.50
c.
$3172.50
A 30-year-old female purchased a 20-Year Endowment insurance policy at the age of 23. The face value of the policy was $78,250. She asks her insurance agent for the extended term nonforfeiture option. Given the table below and the permanent insurance amount of $37.80 per thousand, determine the annual premium and the Extended Term.

a.
Annual Premium of $2,532.10; 31 years and 182 days
c.
Annual Premium of $3,210.23; 37 years and 50 days
b.
Annual Premium of $2,957.85; 26 years and 10 days
d.
Annual Premium of $3,298.54; Life
b.
Annual Premium of $2,957.85; 26 years and 10 days
Your current biweekly gross salary is $1,343.77. You also earn a 7% commission on your monthly sales. If last month you sold $34,000 of product, determine your last month's gross salary pay. (Hint: Assume that there are two pay periods each month.)
a.
$2,687.54
c.
$4,978.32
b.
$2,380.00
d.
$5,067.54
d.
$5,067.54
You are borrowing $3,162 to purchase a scooter using a 36 month installment plan. Determine the annual percentage rate (APR) and the monthly payment given that the interest charge is $425.13. Round your answer to the nearest whole percent and to the nearest cent.
a.
0.08%; $99.77
c.
9%; $114.07
b.
8%; $99.64
d.
10%; $115.75
b.
8%; $99.64
A bank account balance, b, for an account starting with s dollars, earning an annual interest rate, r, and left untouched for n years can be calculated as b=s(1+r)^n Find a bank account balance to the nearest dollar, if the account starts with $200, has an annual rate of 4%, and the money left in the account for 10 years.
a.
$300
c.
$280
b.
$296
d.
$302
b.
$296
XYZ with vertices X(5, 4), Y(3, -1) and Z(0, 2) is translated so that X' is at (3, 1). Choose the coordinates of Y' and Z'.
a.
Y'(5, 2) and Z'(2, 5)
c.
Y'(1, -4) and Z'(-2, -1)
b.
Y'(0, -3) and Z'(-3, 0)
d.
Y'(11, 4) and Z'(8, 6)
c.
Y'(1, -4) and Z'(-2, -1)
Find the perimeter of a regular hexagon with each side measuring 8 meters.
a.
32 m
c.
48 m
b.
80 m
d.
40 m
c.
48 m
Determine the equation for the sine curve that models the D# wave if the

wavelength of D# = 1.106 meters.
c. y= sin(5.68x)
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