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7/24/2019 MA HW 2 (1)h
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Subject Mathematical Analysis, Extended Mathematical Analysis
Assessment type Homework 2
Set on 20151005
Will be collected on 20151026
Tasks prepared by K. Aldoina, M. Kulys
Students name, surname
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Final grade will be counted by dividing gathered number of points by 2 and rounding up to two
decimal places according to the rounding rules.
:2 =
Points
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7/24/2019 MA HW 2 (1)h
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1.One student says: I am sure that the demand given by 3q2ln1qp is elastic with the givenprice of 9 euros. Another student replies: No, its not!Which one is right? Why? (1,5 points)
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2.An investment project has an initial outlay of 30000 euros and in the end of each of the next four
years has returns of 9000 euros. Find the associated internal rate of return. Would you participate in
such investment project, if your preferable internal rate of return is 15%? Why? (2,5 points)
Note:use Newtons method.
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7/24/2019 MA HW 2 (1)h
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3. The amount of nitrogen dioxide, a brown gas that impairs breathing, present in the atmosphere on a
certain June day in the city of Beijing, is approximated by
285,4t25,01
136tA
2
11t0
where A(t) is measured in pollutant standard index (PSI) and t is measured in hours, with 0t
corresponding to 7 a.m. When the PSI increasing and when is it decreasing? At what time is the PSI
highest, and what is its value at that time? (2 points)
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7/24/2019 MA HW 2 (1)h
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4. Supply of potatoes during one concrete week of the year is given by 5x5xlny , and
demand over the same week is given by 11x
3y
(here x is quantity in tons, and y is price in
hundreds euros per ton). Find market equilibrium point. (1,5 points)
Note: use method of bisection; initial interval is 97,3;01,1 ; round the answer up to two decimalplaces.
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7/24/2019 MA HW 2 (1)h
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5.SAULA_TV manufactures middle-size TVs. The quantity x of these TVs demanded each week is
related to the wholesale unit price p by equation 180x006,0p . The weekly total cost incurred
by the factory for producing x units is 60000x120x02,0x000002,0xTC 23 euros. Becauseof technological requirements the factory cant produce less than 4000, and more than 10000 TVs per
week. What should be the level of production per week so that one additionally produced TV would
generate 170 euros of profit? (2 points)
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7/24/2019 MA HW 2 (1)h
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6.An economys consumer price index (CPI) is described by the function 200t4t3,0tI 23
10t0 where 0t corresponds to the year 2000. Find the point of inflection of the function Iand interpret your result. (1,5 points)
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7/24/2019 MA HW 2 (1)h
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7.Approximate the function xlogy 2 by the fourth order polynomial at the point 1x . (2 points)
Note: use Taylors formula.
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7/24/2019 MA HW 2 (1)h
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8.Examine the function1x
4xy
7
2
and draw its graph. (7 points)
Note: in this task you can use any solver to find approximate solutions of the equations.
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7/24/2019 MA HW 2 (1)h
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7/24/2019 MA HW 2 (1)h
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