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Unformatted text preview: FORM C
Math 1743 Fall 2007 Exam II Name: Section #: i.d.#: Instructor: Read all questions careﬁilly and answer them completely. Show appropriate work to receive
maximum credit. In general, if you can label something with units, you should label it with
units. When computing and writing numerical answers, use rounding guidelines discussed in
class and in your text. You will have 75 minutes for the exam and point values are as indicated. 1. In 1991, a lake was stocked with 400 ﬁsh of a new variety. The size of the lake,
availability of food, and other ﬁsh restricted the growth of this population of ﬁsh. Fish po ulations for given years were as follows: (11 points)
Year 1991 1993 1995 1997 1999 2001 2003
1008 1460 1795 2041 2239
a. Find the change in the ﬁsh population between 1997 and 2001.
2041 — 1460 = 581 ﬁsh
b. Find the percentage change in the ﬁsh population between 1999 and 2003. 2239 —1795
1795 100%= 24.7% c. Find the average rate of change in the ﬁsh population between 1993 and 1999. 1795 — 662 ———= 188.83 ﬁsh per year
1999 —1993 2. Two competing banks are offering excellent interest rates on their CDs. The ﬁrst bank
is offering a CD with 6.4% interest compounded continuously, and the second bank is
offering a CD with 6.6% interest compounded quarterly. Determine which bank’s CD is
the better investment by answering the following (round your answers to the hundredths
place as percentages): (8 points) a. Find the effective rate (APY) for the ﬁrst bank’s CD A = Pe°°5‘“ = P(1.0661‘); APY = 6.61% b. Find the effective rate (APY) for the second bank’s CD 0.066
4 4t
A=P[l+ ] =P(1.0677‘); APY=6.77% 2 _
3. For g(t) = %, numerically estimate t1im3g(t) . Show all work in an organized
+ —>— way, including any tables. (8 points) .1399g<t>=10 4. Use the numerical method to ﬁnd the slope of the line tangent to the graph of
f (x) : 3x1/6x — 23 at x = 8. Organize your work in a table (or pair of tables). Although most of the work is done on the calculator, be sure it is clear what values you are
plugging in, and what you are plugging them into. Use the way the numerical method
was presented in class as a guide for your solution here. (11 points) f (8) — f (other endpt)
8 — other endpt 199999999 7999 7.9999
29.30636 29.39064 29.39964 29.39991 secant slope = right endpoint 8.001 8.0001
29.49355 29.40936 29.40094 29.40009 tangent slope = 29.4 5. a. State the formal (limit) deﬁnition of the derivative of a ﬁmction. (5 points) f,(x):1im f(x+h)—f(x) h——>0 h b. If r(x) = ~1.09x2 +12.85x + 1 12.3 1 gives a local restaurant’s revenue (in thousands of dollars), x years since 1988, use the algebraic method (four—step method) to show that
r’(x)= 2.18x + 12.85. (13 points) r(x +h) = —1.09(x +h)2 +12.85(x +h)+112.31
= —1.09x2 — 2.18xh —1.09h2 +12.85x +12.85h +112.31 r,(x) _ lim —1.09X2 — 2.18Xh —1.09h2 +12.85x +12.85h +112.3l— (—1.'09x2 +12.85x + 1 12.31)
h—>0 h _1im—l.09x2 —2.18xh—1.09h2 +12.85x+12.85h+112.31+1.09x2 —12.85x—112.31
h—>0 h —2.18xh—l.09h2 +12.85h h(—2.18x—1.09h+12.85) =lim—————:lim =lim(— 2.18x—l.09h+12.85) h—>0 h h—>0 h h—>0
= 2.18x + 12.85
c. Write an interpretation of r’(7)= 2. 14 (5 points) In 1995, the restaurant’s revenue was decreasing by 2.14 thousand dollars per year. 6. Match the given graph on the leﬁ with its slope graph on the right by writing the appropriate letter in the spaces provided. (21) (13) (0.) (d) (6) (12 points) +
W 7. Use rules and formulas to ﬁnd the derivatives of the following functions. You do not need to simplify your answer. (10 points)
a. g(t) = %+ 54ct — t16 = 9r1 + 54et — t16 g'(t) = 9 —1t'2 + 54ct — 16t15
b. = 4.59 0.65" '= 4.591n 0.65 0.65"
y y 8. In an experiment designed to study memory, a subject was given a list of words to
memorize and asked to recognize these words in a reading sample given after various
elapsed times (see data below). (1‘9 points) Wordsrecognized 70.1 60.5 57.3 54.8 50.9 47.4 41.6
(percentage) a. Find a complete logarithmic model for the data (do not align the input). f (x) = 78.566 — 5 .709 In x percentage of words recognized aﬁer x minutes b. Use rules/formulas to ﬁnd the derivative of the model in part a, writing it as a complete
rate of change model. f ’(x) = 0 — 5.709  1 percentage of words recognized per minute after x minutes X c. Evaluate your rate of change model at an input of 58 and write a complete
interpretation of your answer. f ’(58) = —0.10; After 58 minutes, the percentage of words recognized is decreasing by 0.10 percentage points per minute. ...
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This note was uploaded on 05/04/2008 for the course MATH 1743 taught by Professor Davidsonrossier during the Fall '08 term at The University of Oklahoma.
 Fall '08
 DavidsonRossier

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