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Unformatted text preview: Math 161 Midterm 1 Name: l: . _ _y..U Date: February 2, 2007
Instructor: Dr. Paul Choboter
Time limit: 50 minutes Read all questions carefully, and Show all your work neatly. Calculators, books and notes are not permitted. Good luck! Question Score Points possible 1. In this question, let f(3:) = 952 + 3:1: — 4, and let g(m) = 5x V 39 — 2'
(5 pts) (6.) Simplify the expression f(a: + h) — f
= we“ Jr Sec3% *4 — @14ch "4)
: t _;'l.,'% XL 921%
: Zx‘ﬂ +h7‘ + 3‘0 f (5 pts) (b) Find (fog)(:c). Do not simplify. \/' (C 43 XX.) 3; 2 1— % (:égﬁ —4
‘3 7:2 xvi 2. Suppose that the population of groundhogs1 in a certain park is given by N (t) = 160 x 2“,
where t is measured in years, and t z 0 represents right now. (3 pts) (a) What was the population 2 years ago? (State your answer explicitly in the form of a
single real number.) Na) :\l00x7_”
: \loO x—Z‘; 3 :ugox—L w w.) : 40 StrawMT;
. . J
(3 pts) (b) Write the groundhog population in the form N (t) = 160 x e“ for some expression a.
_ 0.
C? F “00 K 6’ [giléfig_w I a ‘ Man“... a \bO ‘ e a l a 2 12mm) ﬁnllbm a so a e e—Wmm—m J‘L _
0mg“) _ or
bum) dam Luge) : Oi
(4 pts) (c) At what time t will there be 1000 groundhogs? (Leave your answer as an expression
involving terms such as 1n(160). It is necessary to isolate t, but not necessary to simplify
the expression.)
t i_ J #mem.__,...r,mm.“Mummw
\Om —... \em 2 “19000 4%!
ll 3999 : it t \ogz U00 t .m,...W_M—w——»Mmw— ____ w
wee? = W51
logmoo —\09 V00 : twos ’2. HE]le ‘lg Ugo: loop, 1Happy Groundhog Day. \ﬂ’FCll 03 3. Plot the followin functions.
g W1thth {4 pts) (a) Plot f (cc) = 2sin(cr) and g(m) = —cos(3:) on the same set of axes. Clearly label which
curve is f (2:), and which one is (4 pts) (b) Plot = ﬂ and 9(59) = Va: + — 2 on the same set of axes. State how you get the graph of g($;from the graph of f($). gtrﬁ I: We 1; moved 1+ — 7 m0 dcmm the +0???
becauee 09 W‘ﬁ “—
and one WW
\egl on We Xv QXlS
becauee 0% WW ” n undﬂz «he 0“" Mn
L3 addﬁd ‘bo *tWCK. (2 pts) (0) Clearly label the following numbers on the logarithmicscale number line: 0.03, 0.2, 40, 700.
\/ V' t/ l/ 10 (5 pts) 4. (a) Let y = 255—3/2. Use a logarithmic transformation to ﬁnd a linear relationship between
logy and either logs: or I. Determine whether a log10g or a loglinear plot should be used to graph the resulting linear relationship.
—.3 u— 2. V 34* 1
“er mew") v}.
2 5. Evaluate each limit, if it exists, or state that it does not exist. Show your work. (2 pts) (a) lim 32—.— wmwm ka (4+h14+h\ —\ b 5 $+5 $2+2$—15 (4+h)2 — 16 h—ao an
:' has h \0 (Wm) _ ,_— (5 pts) ((1) Let ﬂax) be the function o
% Jam  _ _ 3/
h “7% (x @3 2 E: 3 m 3+0 ._.._ : m WWW“ fr“ WT
ﬁi ﬁw MD
if m < —2
if — 2 S a: < 1 ’1‘ I
if a: > 1
\ A L '37. ‘" ’5 '5 909$ hU’fENSF
(—1314 2 1H 3 ’2. ...
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