MATH 1020
ANSWER KEY TEST 1 VERSION A
Fall 2019
Printed Name: ______________________________ Section #: _______ Instructor:_____________________
Please do not ask questions during this exam. If you consider a question to be ambiguous, state your
assumptions in the margin and do the best you can to provide the correct answer. Refer to the last page for
general directions and calculator troubleshooting tips.
•
Any communication with any person (other than the instructor or the designated proctor) during this
exam in any form, including written, signed, verbal or digital, is understood to be a violation of academic
integrity.
•
All devices, such as computers, cell phones, cameras, watches and PDAs must be turned off and stowed
away while the student is in the testing room.
•
The only calculators to be used are TI-83, TI-83+, or TI-84+. You may NOT borrow or share a calculator
with another person taking this test.
•
Statement of Academic Integrity: I have not and will not give or receive improper aid on this test.
In signing below, I acknowledge that I have read, understand, and agree to these testing conditions.
Student’s Signature: _________________________________________________________________
(This test will not be accepted for grading unless it bears the signature of the student.)
Possible
Points
FR#1
FR #2
FR #3
FR #4
FR#5
Scantron
Free
Response
Total
Multiple
Choice
Total
Total
8
4
9
4
8
1
34
66
100
Points
Earned
Page 1/11
MATH 1020
ANSWER KEY TEST 1 VERSION A
Fall 2019
MULTIPLE CHOICE: 66 points
Use a #2 pencil and completely fill each bubble on your scantron to answer each multiple choice question.
(For future reference, circle your answers on this test paper.) There is no penalty for guessing on multiple
choice. If you indicate more than one answer, or you leave a blank, the question will be marked as
incorrect. Each question is worth 3 points, unless otherwise indicated.
B
D
A
D
B
C
A
B
D
B
C
A
B
A
C
D
C
B
D
A
A
C
_____________________________________________________________________________________
1.
In 1999 there were 34.742 thousand new cases of Leukemia. From 1999 until 2016, the number of
Leukemia cases has increased by 1.01 thousand new cases per year.
Write a completely defined model for the given information.
a.=
L( x) 34.742 x + 1.01 thousand cases gives the number of new Leukemia cases, x years since
1999, 0 ≤ x ≤ 17 .
b.
L=
( x) 1.01x + 34.742 thousand cases gives the number of new Leukemia cases, x years since
1999, 0 ≤ x ≤ 17 .
c.
L=
( x) 1.01x + 34.742 thousand cases gives the number of new Leukemia cases, x years since
1999, 1999 ≤ x ≤ 2016 .
d.=
L( x) 34.742 x + 1.01 thousand cases gives the number of new Leukemia cases, x years since
1999, 1999 ≤ x ≤ 2016 .
2. Which one of the following does NOT describe a function?
a. The surface area of a sphere is equal to four times pi times the square of the radius of the sphere.
b. The cumulative sales of Examplesoft products are given by s=
(t ) 300t + 1000 units where t is the
number of years since 2003. 0 ≤ t ≤ 12 .
c.
x
1
2
3
4
5
f ( x)
1
1
2
3
5
d.
r
1
1
2
2
3
g (r )
-2
2
-6
6
-9
Page 2/11
C
MATH 1020
ANSWER KEY TEST 1 VERSION A
Fall 2019
_________________________________________________________________________________________
Use the given information for the next three questions.
[2 pts each]
C (t ) =
−0.067t + 1.119 million cars gives the number of cars that were stolen in the US, t years since 2005,
Checkpoint: C (2) = 0.985
0≤t ≤9.
3. State and interpret the slope of the equation in the above model.
a. -0.067; The number of cars stolen decreased by 0.067 million cars per year between 2005 and 2014.
b. -0.067; In 2005, there were 0.067 million cars stolen in the US.
c. 1.119; The number cars stolen increased by 1.119 million cars per year between 2005 and 2014.
d. 1.119; In 2005, there were 1.119 million cars stolen in the US.
4. State and interpret the y-intercept of the equation in the above model.
a. -0.067; The number of cars stolen decreased by 0.067 million cars per year between 2005 and 2014.
b. -0.067; In 2005, there were 0.067 million cars stolen in the US.
c. 1.119; The number cars stolen increased by 1.119 million cars per year between 2005 and 2014.
d. 1.119; In 2005, there were 1.119 million cars stolen in the US.
5. How many cars were stolen in 2010? Does this question use extrapolation or interpolation?
a. 0.784 million cars; Extrapolation
b. 0.784 million cars; Interpolation.
c. 0.449 million cars; Extrapolation.
d. 0.449 million cars; Interpolation.
_________________________________________________________________________________________
6. For a function g ( x) that is continuous everywhere on its domain (−∞, ∞) , lim g ( x) = 0 means that the
graph of g ( x) _____________________.
x →∞
a. increases without bound as x-values approach 0
b. has a vertical asymptote
c. has a horizontal asymptote
d. increases without bound as x-values increase without bound
Page 3/11
MATH 1020
ANSWER KEY TEST 1 VERSION A
Fall 2019
_______________________________________________________________________________________
Use the given information for the next two questions.
(
Atmospheric pressure is given
by p ( x) 101, 325.0 1 − 2.256(10−5 ) x
=
meters, 0 ≤ x ≤ 15, 000 .
)
5.256
Pascals where x is the altitude in
Checkpoint: p (1, 000) = 89,873.203
7. Complete the following statements by filling in the blanks.
The input units are ___________________ and input description is ___________________________.
The output units are __________________ and output description is _________________________.
a. Meters, altitude;
Pascals, atmospheric pressure
b. Meters, atmospheric pressure;
Pascals, altitude
c. Pascals, atmospheric pressure;
Meters, altitude
d. Pascals, altitude;
Meters, atmospheric pressure
8. Use the calculator to examine the graph of p ( x) on the given input data range. Describe the direction
and concavity of the graph.
a. decreasing and concave down
b. decreasing and concave up
c. increasing and concave down
d. increasing and concave up
_________________________________________________________________________________________
9. Consider the two given functions. Choose the exponential decay function and then find the percentage
change for the exponential decay function.
f ( x) = 0.092(0.334) x
a. 4.5%
b. -33.4%
g ( x) = 0.531(1.045) x
c. -90.8%
d. -66.6%
10. The number of bowling shoes sold in the US was 1.2 million units in 2015, but the quantity sold decreased
by approximately 2.9% each year between 2015 and 2018.
Find the best equation to complete the following model.
__________________________________million units gives the number of bowling shoes sold in the US,
x years since 2015, 0 ≤ x ≤ 4 .
a. S ( x) = 1.2(1.029)
x
c. S ( x=
) 1.2 − 1.029 x
b. S ( x) = 1.2(0.971)
x
d. S=
( x) 1.2 x − 0.029
Page 4/11
MATH 1020
ANSWER KEY TEST 1 VERSION A
Fall 2019
_________________________________________________________________________________________
Use the given information for the next two questions.
In a certain lake, the bass feed primarily on minnows and the minnows feed on plankton. The size of the bass
population is f (n) bass where n is the number of minnows in the lake. The size of the minnow population is
n( x) minnows where x is the number of plankton in the lake.
11. Which one of the following functions represents a meaningful new function from the given functions?
a. f (n) ⋅ n( x)
b. f (n) + n( x)
c. f (n( x))
d. n( x( f ))
12. What are the output units for the new meaningful function?
a. Bass
b. Minnows
c. Plankton
d. Bass per plankton
_________________________________________________________________________________________
Use the given information for the next two questions.
13. At a certain coffee shop, yearly sales of French-vanilla lattes can be modeled as S ( x) hundred lattes,
when the price is x dollars per latte. What is the yearly revenue from the sale of French-vanilla lattes?
a. S ( x)
b. x ⋅ S ( x)
c.
S ( x)
x
d. x + S ( x)
14. What are the output units for the yearly revenue from the sale of French-vanilla lattes?
a. hundred dollars
b. hundred lattes
c. dollars
d. dollars per latte
________________________________________________________________________________________
Page 5/11
MATH 1020
ANSWER KEY TEST 1 VERSION A
15. What does the table suggest that
Fall 2019
lim g ( x) =_____________ ?
x
g ( x)
2.9
4.01
2.99
4.001
2.999
4.0001
2.9999
4.00001
x →3−
a. 2
b. 3
c. 4
d. does not exist
16. The table below gives the population of the world at various time during the 20th century and can be used
to find an exponential function p (t ) that models the world population p in year t .
Year
1910
1930
1950
1970
1990
Population
(million people)
1750
2070
2520
3700
5300
Find a logarithmic function that models the inverse of p (t ) .
a. t ( p ) =
−640,392.039 + 84,939.844 ln( p )
b. t ( p ) = 1,887.282(1.0000106215 )
p
−9
c. t ( p ) = 4.047(10 )(1.014 )
P
d. t ( p ) 1,399.785 + 69.251ln( p )
=
17. Which one of the functions could have lim+ f ( x) = −∞ and lim f ( x) = ∞ ?
x→ 0
a. linear
b. cubic
x→ ∞
c. logarithmic
d. logistic
Page 6/11
MATH 1020
ANSWER KEY TEST 1 VERSION A
Fall 2019
_____________________________________________________________________________________
Use the given graph of f ( x) to answer the next two questions.
18. Explain mathematically why f ( x) has a vertical asymptote at x = 2.
a. lim− f ( x) does not exist
x→2
b. lim+ f ( x) = −∞
x→2
c. lim f ( x) = 2
x →∞
d. lim f ( x) = 2
x →−∞
19. f ( x) is not continuous at x = −4 because _______________________________.
a. f (−4) is undefined
b. lim − f ( x) does not exist
c. lim + f ( x) does not exist
d. lim − f ( x) ≠ lim + f ( x)
x→ −4
x→ −4
x→ −4
x→ −4
________________________________________________________________________________________
2
20. Which of the following statements is TRUE about a function of the form f ( x) = ax + bx + c for a < 0 ?
a. The output values increase to a maximum value and then decrease.
b. The graph changes concavity from concave down to concave up.
c. The graph has a horizontal asymptote.
d. The outputs value increase without bound as x increases without bound.
Page 7/11
MATH 1020
ANSWER KEY TEST 1 VERSION A
Fall 2019
_______________________________________________________________________________________
Use the given information for the next two questions.
The spread of virus through a student population can be modeled by V (d ) =
300.525
, where
1 + 4,999.0 e −0.8 d
V (d ) is the total number of students infected after d days, 5 ≤ d ≤ 20 .
Checkpoint: V (2) = 0.297
21. It appears that there exists a day where the number of students infected was increasing most rapidly.
This can be verified on the graph of V by taking note of____________________________.
a. the change in concavity from concave up to concave down, as the number of days increase.
b. the change in concavity from concave down to concave up, as the number of days increase.
c. the maximum value.
d. the end behavior of V .
22. The function V (d ) =
300.525
has horizontal asymptotes _______________________.
1 + 4,999.0 e −0.800 d
a. y 4,999.0;
=
=
y 0
b. y 300.525;
=
=
y 4,999.0
c.=
y 0;=
y 300.525
d.=
y 0;=
y 0.800
_______________________________________________________________________________________
23. The table below shows a company’s profit from the sale of sport utility vehicles (SUVs). Describe the
behavior suggested by the scatter plot of the data and list the type of function(s) that best exhibit this
behavior.
SUVs (in millions)
10
20
30
40
50
60
Profit (in trillion
dollars)
0.9
3.1
4.3
5.2
5.8
6.2
a. The scatter plot of the data is increasing and has no concavity is shown; linear.
b. The scatter plot is increasing and is concave up; quadratic or exponential growth.
c. The scatter plot of the data is increasing and is concave down; logarithmic or quadratic.
d. The scatter plot is increasing and appears to have an inflection point; cubic or logistic.
Page 8/11
MATH 1020
ANSWER KEY TEST 1 VERSION A
Fall 2019
FREE RESPONSE: 34 points
Show work where possible. Read the directions at the back of the test on rounding, inclusion of units, and
writing models and sentences.
1.
r (t=
) 0.5t 2 − 2t + 5 million dollars gives the cumulative revenue for Widgit Company, LLC, where t is the
number of years since the start of the business at the end of 2000, 3 ≤ t ≤ 18 .
Checkpoint: r (2) = 3
a. When, after the start of the business, did cumulative revenue first hit 70 million
dollars? Find the answer correct to three decimal places.
a. 2 pts first blank;
2 pts second blank
b. 2 pts
c. 2 pts
Note: A negative solution to the equation doesn’t make sense in the context of
the problem.
__13.576 ___
In what month and year did the cumulative revenue first hit 70 million dollars? __July 2014__
Since 0.576x12=6.912
b. According to the model, what is the predicted cumulative revenue for Widgit Company, LLC at the
end of 2020? Round to three decimal places and include units with the answer.
165.000 million dollars, since r (20) = 165
c. Write the following statement in function notation.
At the end of 2004 the cumulative revenue earned by WidgitCo was 5 million dollars.
r (4) = 5
( _______ / 8 pts )
2. P (c) billion units gives the production level at a factory, when c million dollars in capital is invested.
Write a sentence of interpretation for P (10) = 27.982 .
When 10 million dollars in capital is invested, the production level at a factory
is 27.982 billion units.
1 pt when
1 pt what
2 pt how much, with units
( _______ / 4 pts )
Page 9/11
MATH 1020
ANSWER KEY TEST 1 VERSION A
Fall 2019
3. Solar power has seen much growth in the recent past. The table show the number of US solar
photovoltaic (PV) installations (residential, non-residential and utilities), which are a type of solar energy
generator.
Year
2006
2008
2010
2012
2014
Solar PV installations, in
thousands
0.105
0.298
0.852
2.388
6.201
a.
Look at scatter plot of the data. How many concavities are suggested by the scatter plot of the data?
Circle one:
0
1
2
b. Align the input to the number of years since 2000. Write a completely defined exponential model for
the newly aligned data.
Part a) 1 pt
Part b) 4 pts function equation
1 pt output units
f ( x) = 0.005(1.668x ) thousand installations gives the number of solar
1 pt output description
1.5 pt input units and
PV installations in the US homes, x years since 2000, 6 ≤ x ≤ 14 .
description
0.5 pts input data range
( _______ / 9 pts )
4. Fill in the blanks using as many of the six functions that apply.
Linear
Exponential
Logarithmic
Quadratic
Cubic
Logistic
a. Name any and all of the functions that have exactly one vertical asymptote:
_____LOGARITHMIC_____________________________________
a. 2 pts
b. 2 pts.
b. Name any and all of the functions that have exactly one horizontal asymptote:
____EXPONENTIAL_______________________________________
( _______ / 4 pts )
Page 10/11
MATH 1020
ANSWER KEY TEST 1 VERSION A
Fall 2019
5. Refer to the graph of f ( x) , graphed below on (−∞, ∞) , to answer the following questions. For part f),
write an answer of ∞ , −∞ , or a number L, if appropriate. If the answer “does not exist” or is
“undefined”, write “dne”.
a. Mark an “X” directly on the graph (not the x-axis) at any and all inflection points
b. Name all intervals on which the function is increasing. (15,125 )
c. Name all intervals on which the function is decreasing. ( −∞,15 ) , (125, ∞ )
d.
Name all intervals on which the function is concave up. ( −∞, 70 )
a. 1 pt
b. 1 pt
c. 2 pts
d. 1 pt
e. 1 pt
f. 2 pts
e. Name all intervals on which the function is concave down. ( 70, ∞ )
f.
Find the limits: lim f ( x) = __ ∞ ___
x → −∞
and
lim f ( x) = __ − ∞ ___
x→ ∞
( _______ / 8 pts )
6. A scantron correctly bubbled with a #2 pencil, a correctly-bubbled XID, a correctly-bubbled test version,
AND a signed academic integrity statement (on the front of the test) earns 1 point.
--- END OF TEST -Page 11/11
MATH 1020
ANSWER KEY TEST 1 VERSION A
Fall 2019
General Directions:
•
Show work where possible. Answers without supporting work (where work is appropriate) may receive
little credit.
•
Do not round intermediate calculations.
•
Answers in context ALWAYS require units.
•
Assume end of the year data unless stated otherwise.
•
Round your answers to 3 decimal places UNLESS the answer needs to be rounded differently to make
sense in the context of the problem OR the directions specify another type rounding OR the complete
answer has fewer than 3 decimal places.
•
When asked to write a model, include all components of a model: an equation, a description of the input
including units, a description of the output including units, and the input interval when known.
•
When asked to write a sentence of practical interpretation, answer the questions: when?, what?, and
how much? using ordinary, conversational language. DO NOT use math words, terms, or unnecessary
phrases.
•
Always use a ruler when estimating values off of a graph.
HINTS FOR TROUBLESHOOTING YOUR CALCULATOR:
•
If you lose your L1, L2, etc., you may reinsert them using STAT 5 (set-up editor) enter.
•
The SCATTER PLOT will not show unless Plot 1 has been turned on and there is data in L1 and L2.
•
ZOOM 0 may not work for graphing if Plot 1 is turned on.
•
DIM MISMATCH error usually means that the lists in L1 and L2 are not of equal length.
•
DATA TYPE error usually means that you already have something in Y1 and you need to clear it before you can paste a
new equation.
•
INVALID DIM error usually means that your plot(s) are on, but that you have no data in the lists. Refer to the second
hint above.
•
If your batteries die, raise your hand and hold up your calculator. If your instructor has an extra calculator available,
he/she will loan it to you for a few minutes.
•
SYNTAX ERROR: Try GO TO. This will happen if you use a subtraction minus sign when you should use a negative
sign.
•
MATH SOLVER only works if there is a variable “x” in Y1.
•
If you need to CLEAR MEMORY, use 2nd +, 7:Reset, 1:All Ram, 2:Reset
Page 12/11