This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 1743 Fall 2007 Exam HI FORM C Name: Key Section #: i.d.#: Instructor: Read all questions carefully 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 unless the problem speciﬁes otherwise. Every model you
write (and that includes rate of change models) should be complete. You will have 75 minutes for the exam and point values are as indicated. 1. Suppose that the population of a certain collection of Brazilian ants is given by
A(t) = (t + 300) In (t + 4) ants after t days. (15 points) a. Find the complete rate of change model for the population of the ants, A'(t). A(t) = (1).1n(t +4)+ (t +300). “+4 :1n(t+4)+ trio ants per day, aﬁer t days. b. What was the ant population after 20 days? A(20) = 1016.98; 1016 or 1017 ants c. Find and interpret A’(20). A’(20)= 16.5;
After twenty days, the collection of ants was growing by 16.5 ants per day. 0n problems 2—4, you do n_ot need to simplzﬁ/ your answers.
2. Given g(x) = 79K + (9 — x)7, ﬁnd g’(x). (8 points) g’(x) = (1n 7)79x 9+ 7(9—x)6 —1 3. Given S(p) = 65.823p(0.904p), ﬁnd S'(p). (8 points) S'(p) = 65.823~1(0.904p)+65.823p~1n 0.904(0.904P) 4. Given v(x) = xikﬂ ﬁnd Q (11 points)
e (In x) dx v(x) = 37e‘x  (In x)—6 V'(x) = 37e‘x —1  (In x)"6 + 37e’” —6 (In x)‘7 i
X 01‘ v(x) = 37(ex  (1n X)6 )—1 V'(x) = 37 —1(ex (1n x)6 )_2 [ex  (In x)6 + ex 6(ln x)5 l) 5. The weekly weight loss of a person on a weightloss program is given by
w(t) = 1.58te‘°'lgt pounds after t weeks on the program. (17 points) In parts a & b, give both input and output, round coordinates to the hundredths place, and
please label them with units. a. Find the absolute maximum weekly weight loss between weeks three and eight on the
program. t = 5.56 weeks w = 3.23 pounds b. Find the absolute minimum weekly weight loss between weeks three and eight on the program. t = 3 weeks w = £2.76 pounds 0. Based on your answers to the questions above, ﬁll in the following: On the interval [3, 8], w’(t) is positive between t = 3 and t = 5.56 . On the interval [3, 8], w'(t) is negative between t = 5.56 and t = 8 . 6. A soda bottling company bottles 15,000 cases of orange soda each year. The cost to
set up the machine for a production run is $1300, and the cost to store a case for one year
is $12. (19 points) a. If x is the number of cases in production run, write an expression representing the
number of production runs necessary to produce 15,000 cases. 15000
x b. Write an expression for the total set up cost. [15000](1300) X c. Assume that the average number of cases stored throughout the year is half the number
of cases in production run. Write an expression for the total storage cost for one year,
using x as the number of cases in each production run. a» (1. Use your responses to parts b & c to write a complete model for the combined set up
and storage costs for one year. C(X) = (15000](1300)+[%)(12) = W + 6x dollars, where x cases are in each
x x production run. e. What size production run minimizes the total yearly cost? Show some work (i.e.
calculus) to support your answer. Round to the nearest whole number. C(x) =19500000x—1 + 6x ; C’(x) = —19500000x—2 + 6 =0 x = 1802.78; 1802 or 1803 cases f. How many production runs will minimize total yearly production cost? Round to the
nearest tenth, assuming they can make a partial run to end up with 15,000 cases. 8.3 runs 7. An international wildlife agency determined that the population of Ozark bigcared bat
for given years is:
(22 points) 1972 . 1977 1982 1987 1992 1997 2002
Ozark big—eared bats 87.5 81.4 63.2 39.8 22.7 18.9 17.0
(thousand bats) a. Find a complete logistic model for this data. Align the data so that the year 1972
corresponds to an input of zero. 114.257 f x 2——
( ) 1+O.26le°'l23x thousand bats, x years after 1972 =114.257(1+ 026161123")—1 b. Find the complete model for rate of change of the number of population of Ozark big
eared bats. f’(x) = 114.257  —1(1+ 0.261e0'123" )‘2 0.261e°“23"  0.123 = —3.668e°‘123x (1 + 0.261e0'123x )_2 thousand bats per year, x years aﬁer 1972 c. Find the inﬂection point for the model you generated in part a. Round both coordinates
to the hundredths place and label them with appropriate units. x = 10.96 years after 1972; f = 57.12 thousand bats ...
View
Full Document
 Fall '08
 DavidsonRossier

Click to edit the document details