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Q141 Exponential Functions Applied/Contextual Exponential Modeling View

Assume that a type of eucalyptus has an expected exponential growth rate in the first years after planting, modeled by the function $y(t) = a^{t-1}$, in which $y$ represents the height of the plant in meters, $t$ is considered in years, and $a$ is a constant greater than 1. The graph represents the function $y$.
Also assume that $y(0)$ gives the height of the seedling when planted, and it is desired to cut the eucalyptus when the seedlings grow 7.5 m after planting.
The time between planting and cutting, in years, is equal to
(A) 3.
(B) 4.
(C) 6.
(D) $\log_{2} 7$.
(E) $\log_{2} 15$.

Q144 Stationary points and optimisation Geometric or real-world application leading to a quadratic equation View

To prevent an epidemic, the Health Department of a city disinfected all neighborhoods to prevent the spread of the dengue mosquito. It is known that the number $f$ of infected people is given by the function $f(t) = -2t^{2} + 120t$ (where $t$ is expressed in days and $t = 0$ is the day before the first infection) and that this expression is valid for the first 60 days of the epidemic.
The Health Department decided that a second disinfection should be done on the day when the number of infected people reached 1600 people, and a second disinfection had to take place.
The second disinfection began on
(A) the $19^{\text{th}}$ day.
(B) the $20^{\text{th}}$ day.
(C) the $29^{\text{th}}$ day.
(D) the $30^{\text{th}}$ day.
(E) the $60^{\text{th}}$ day.

Q147 Simultaneous equations View

The figure shows three lines in the Cartesian plane, with $P, Q$ and $R$ being the intersection points between the lines, and $A, B$ and $C$ being the intersection points of these lines with the $x$-axis.
This figure is the graphical representation of a linear system of three equations and two unknowns that
(A) has three distinct real solutions, represented by points $P, Q$ and $R$, since they indicate where the lines intersect.
(B) has three distinct real solutions, represented by points $A, B$ and $C$, since they indicate where the lines intersect the $x$-axis.
(C) has infinitely many real solutions, since the lines intersect at more than one point.
(D) has no real solution, since there is no point that belongs simultaneously to all three lines.
(E) has a unique real solution, since the lines have points where they intersect.

Q148 Stationary points and optimisation Geometric or applied optimisation problem View

Having a large piece of land, an entertainment company intends to build a rectangular space for shows and events, as shown in the figure.
The area for the public will be fenced with two types of materials:

on the sides parallel to the stage, a type A screen will be used, more resistant, whose value per linear meter is $\mathrm{R}\$ 20.00$;
on the other two sides, a type B screen will be used, common, whose linear meter costs $\mathrm{R}\$ 5.00$.

The company has $\mathrm{R}\$ 5000.00$ to buy all the screens, but wants to do it in such a way that it obtains the largest possible area for the public.
The quantity of each type of screen that the company should buy is
(A) $50.0 \mathrm{~m}$ of type A screen and $800.0 \mathrm{~m}$ of type B screen.
(B) $62.5 \mathrm{~m}$ of type A screen and $250.0 \mathrm{~m}$ of type B screen.
(C) $100.0 \mathrm{~m}$ of type A screen and $600.0 \mathrm{~m}$ of type B screen.
(D) $125.0 \mathrm{~m}$ of type A screen and $500.0 \mathrm{~m}$ of type B screen.
(E) $200.0 \mathrm{~m}$ of type A screen and $200.0 \mathrm{~m}$ of type B screen.

Q149 Solving quadratics and applications Compute Partial Sum of an Arithmetic Sequence View

A club has a soccer field with a total area of $8000 \mathrm{~m}^{2}$, corresponding to the grass. Usually, the grass mowing of this field is done by two machines owned by the club for this service. Working at the same pace, the two machines mow together $200 \mathrm{~m}^{2}$ per hour. Due to the urgency of holding a soccer match, the field administrator will need to request machines from the neighboring club equal to his own to do the mowing work in a maximum time of 5 h.
Using the two machines that the club already has, what is the minimum number of machines that the field administrator should request from the neighboring club?
(A) 4
(B) 6
(C) 8
(D) 14
(E) 16

Q150 Variable acceleration (1D) Compute Partial Sum of an Arithmetic Sequence View

A passion fruit producer uses a water tank with volume $V$ to feed the irrigation system of his orchard. The system draws water through a hole at the bottom of the tank at a constant flow rate. With the water tank full, the system was activated at 7 a.m. on Monday. At 1 p.m. on the same day, it was found that 15\% of the water volume in the tank had already been used. An electronic device interrupts the system's operation when the remaining volume in the tank is 5\% of the total volume, for refilling.
Assuming that the system operates without failures, at what time will the electronic device interrupt the operation?
(A) At 3 p.m. on Monday.
(B) At 11 a.m. on Tuesday.
(C) At 2 p.m. on Tuesday.
(D) At 4 a.m. on Wednesday.
(E) At 9 p.m. on Tuesday.

Q151 Inequalities Linear Programming (Optimize Objective over Linear Constraints) View

A region of a factory must be isolated, as employees are exposed to accident risks there. This region is represented by the gray portion (quadrilateral with area S) in the figure.
So that employees are informed about the location of the isolated area, informational posters will be posted throughout the factory. To create them, a programmer will use software that allows drawing this region from a set of algebraic inequalities.
The inequalities that should be used in the said software for drawing the isolation region are
(A) $3y - x \leq 0 ; 2y - x \geq 0 ; y \leq 8 ; x \leq 9$
(B) $3y - x \leq 0 ; 2y - x \geq 0 ; y \leq 9 ; x \leq 8$
(C) $3y - x \geq 0 ; 2y - x \leq 0 ; y \leq 9 ; x \leq 8$
(D) $4y - 9x \leq 0 ; 8y - 3x \geq 0 ; y \leq 8 ; x \leq 9$
(E) $4y - 9x \leq 0 ; 8y - 3x \geq 0 ; y \leq 9 ; x \leq 8$

Q152 Vectors Introduction & 2D Vector Word Problem / Physical Application View

A group of junior scouts, in an activity at the city park where they live, set up a tent as shown in the photo in Figure 1. Figure 2 shows the diagram of this tent's structure, in the form of a right prism, in which metal rods were used.
After assembling the rods, one of the scouts observed an insect moving on them, starting from vertex $A$ toward vertex $B$, from there toward vertex $E$ and, finally, made the journey from vertex $E$ to $C$. Consider that all these movements were made by the shortest distance path between the points.
The projection of the insect's displacement on the plane containing the base $ABCD$ is given by (see answer options with figures).

Q155 Probability Definitions Finite Equally-Likely Probability Computation View

A box contains a $\mathrm{R}\$ 5.00$ bill, a $\mathrm{R}\$ 20.00$ bill, and two $\mathrm{R}\$ 50.00$ bills of different designs. A bill is randomly drawn from this box, its value is noted, and the bill is returned to the box. Then, the previous procedure is repeated.
The probability that the sum of the noted values is at least equal to $\mathrm{R}\$ 55.00$ is
(A) $\frac{1}{2}$
(B) $\frac{1}{4}$
(C) $\frac{3}{4}$
(D) $\frac{2}{9}$
(E) $\frac{5}{9}$

Q156 Data representation View

A company recorded its performance in a given year through the graph, with monthly data of total sales and expenses.
Monthly profit is obtained by subtracting expenses from total sales, in that order.
Which three months of the year had the highest profits recorded?
(A) July, September, and December.
(B) July, September, and November.
(C) April, September, and November.
(D) January, September, and December.
(E) January, April, and June.

Q157 Probability Definitions Probability Using Set/Event Algebra View

A couple, both 30 years old, intends to take out a private pension plan. The insurance company researched, to define the value of the monthly contribution, estimates the probability that at least one of them will be alive in 50 years, based on population data, which indicate that 20\% of men and 30\% of women today will reach the age of 80.
What is this probability?
(A) $50\%$
(B) $44\%$
(C) $38\%$
(D) $25\%$
(E) $6\%$

Q160 Measures of Location and Spread View

The graph shows the average daily oil production in Brazil, in million barrels, in the period from 2004 to 2010.
Estimates made at that time indicated that the average daily oil production in Brazil in 2012 would be 10\% higher than the average of the three last years shown in the graph.
If these estimates had been confirmed, the average daily oil production in Brazil, in million barrels, in 2012, would have been equal to
(A) 1.940.
(B) 2.134.
(C) 2.167.
(D) 2.420.
(E) 6.402.

Q161 Exponential Functions Applied/Contextual Exponential Modeling View

The government of a city is concerned about a possible epidemic of an infectious disease caused by bacteria. To decide what measures to take, it must calculate the reproduction rate of the bacteria. In laboratory experiments of a bacterial culture, initially with 40 thousand units, the formula for the population was obtained:
$$p(t) = 40 \cdot 2^{3t}$$
where $t$ is the time, in hours, and $p(t)$ is the population, in thousands of bacteria.
In relation to the initial quantity of bacteria, after 20 min, the population will be
(A) reduced to one third.
(B) reduced to half.
(C) reduced to two thirds.
(D) doubled.
(E) tripled.

Q162 Measures of Location and Spread View

A cable TV subscription seller had, in the first 7 months of the year, a monthly average of 84 subscriptions sold. Due to a company restructuring, all sellers were required to have, at the end of the year, a monthly average of 99 subscriptions sold. Faced with this, the seller was forced to increase his monthly sales average in the remaining 5 months of the year.
What should be the seller's monthly sales average in the next 5 months so that he can meet his company's requirement?
(A) 91
(B) 105
(C) 114
(D) 118
(E) 120

Q165 Circles Circles Tangent to Each Other or to Axes View

Bowls is a sport played on courts, which are flat and level grounds, limited by perimeter wooden boards. The objective of this sport is to throw bowls, which are balls made of synthetic material, in such a way as to place them as close as possible to the jack, which is a smaller ball made, preferably, of steel, previously thrown. Suppose that a player threw a bowl with radius 5 cm that ended up touching the jack with radius 2 cm, as illustrated in Figure 2.
Consider point $C$ as the center of the bowl, and point $O$ as the center of the jack. It is known that $A$ and $B$ are the points where the bowl and the jack, respectively, touch the ground of the court, and that the distance between $A$ and $B$ is equal to $d$. Under these conditions, what is the ratio between $d$ and the radius of the jack?
(A) 1
(B) $\frac{2\sqrt{10}}{5}$
(C) $\frac{\sqrt{10}}{2}$
(D) 2
(E) $\sqrt{10}$

Q166 Arithmetic Sequences and Series Find a Specific Coefficient in a Single Binomial Expansion View

In a school project, João was invited to calculate the areas of several different squares, arranged in sequence, from left to right, as shown in the figure.
The first square in the sequence has a side measuring 1 cm, the second square has a side measuring 2 cm, the third square has a side measuring 3 cm, and so on. The objective of the project is to identify by how much the area of each square in the sequence exceeds the area of the previous square. The area of the square that occupies position $n$ in the sequence was represented by $\mathrm{A}_{n}$.
For $n \geq 2$, the value of the difference $\mathrm{A}_{n} - \mathrm{A}_{n-1}$, in square centimeter, is equal to
(A) $2n - 1$
(B) $2n + 1$
(C) $-2n + 1$
(D) $(n-1)^{2}$
(E) $n^{2} - 1$

Q167 Inequalities Limit Reading from Graph View

Some electronic equipment can ``burn out'' during operation when its internal temperature reaches a maximum value $\mathrm{T}_{\mathrm{M}}$. For greater durability of its products, the electronics industry connects temperature sensors to this equipment, which activate an internal cooling system, turning it on when the temperature of the electronic device exceeds a critical level $\mathrm{T}_{\mathrm{c}}$, and turning it off only when the temperature drops to values below $\mathrm{T}_{\mathrm{m}}$. The graph illustrates the oscillation of the internal temperature of an electronic device during the first six hours of operation, showing that its internal cooling system was activated several times.
How many times did the temperature sensor activate the system, turning it on or off?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 9

Q168 Permutations & Arrangements Linear Arrangement with Constraints View

To stimulate his daughter's reasoning, a father made the following drawing and gave it to the child along with three colored pencils. He wants the girl to paint only the circles, so that those connected by a segment have different colors.
In how many different ways can the child do what the father asked?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 72

Q172 Curve Sketching Identifying the Correct Graph of a Function View

A pharmaceutical company conducted a study of the efficacy (in percentage) of a medication over 12 hours of treatment in a patient. The medication was administered in two doses, with a 6-hour interval between them. As soon as the first dose was administered, the medication's efficacy increased linearly for 1 hour, until reaching maximum efficacy (100\%), and remained at maximum efficacy for 2 hours. After these 2 hours at maximum efficacy, it began to decrease linearly, reaching 20\% efficacy upon completing the initial 6 hours of analysis. At this moment, the second dose was administered, which began to increase linearly, reaching maximum efficacy after 0.5 hours and remaining at 100\% for 3.5 hours. In the remaining hours of analysis, the efficacy decreased linearly, reaching 50\% efficacy at the end of treatment.
Considering the quantities time (in hours) on the horizontal axis and medication efficacy (in percentage) on the vertical axis, which graph represents this study?
(A), (B), (C), (D), (E) [see figures]

Q173 Simultaneous equations Inequality Word Problem (Applied/Contextual) View

A rectangular plot of land with sides whose measurements, in meters, are $x$ and $y$ will be fenced for the construction of an amusement park. One side of the plot is located on the banks of a river. Observe the figure.
To fence the entire plot, the owner will spend R\$ 7500.00. The fence material costs R\$ 4.00 per meter for the sides of the plot parallel to the river, and R\$ 2.00 per meter for the other sides.
Under these conditions, the dimensions of the plot and the total cost of the material can be related by the equation
(A) $4(2x + y) = 7500$
(B) $4(x + 2y) = 7500$
(C) $2(x + y) = 7500$
(D) $2(4x + y) = 7500$
(E) $2(2x + y) = 7500$

Q174 Geometric Sequences and Series Applied Geometric Model with Contextual Interpretation View

To celebrate a city's anniversary, the city council organizes four consecutive days of cultural attractions. Experience from previous years shows that, from one day to the next, the number of visitors to the event is tripled. 345 visitors are expected for the first day of the event.
A possible representation of the expected number of participants for the last day is
(A) $3 \times 345$
(B) $(3 + 3 + 3) \times 345$
(C) $3^{3} \times 345$
(D) $3 \times 4 \times 345$
(E) $3^{4} \times 345$

Q178 Measures of Location and Spread View

A person is competing in a selection process for a job opening in an office. In one of the stages of this process, he must type eight texts. The number of errors made by this person in each of the typed texts is given in the table.

Text	\begin{tabular}{ c } Number
of errors

\hline I & 2 \hline II & 0 \hline III & 2 \hline IV & 2 \hline V & 6 \hline VI & 3 \hline VII & 4 \hline VIII & 5 \hline \end{tabular}
In this stage of the selection process, candidates will be evaluated by the median value of the number of errors.
The median of the number of errors made by this person is equal to
(A) 2{,}0.
(B) 2{,}5.
(C) 3{,}0.
(D) 3{,}5.
(E) 4{,}0.

Q180 Normal Distribution Determining coefficients from given conditions on function values or geometry View

The Body Mass Index (BMI) can be considered a practical, easy and inexpensive alternative for direct measurement of body fat. Its value can be obtained by the formula $\text{BMI} = \frac{\text{Mass}}{(\text{Height})^{2}}$, in which mass is in kilograms and height is in meters. Children naturally begin life with a high body fat index, but become thinner as they age, so scientists created a BMI especially for children and young adults, from two to twenty years of age, called BMI by age.
The graph shows the BMI by age for boys.
A mother decided to calculate the BMI of her son, a ten-year-old boy, with 1.20 m height and $30.92 \mathrm{~kg}$.
To be in the range considered normal for BMI, the minimum and maximum values that this boy needs to lose weight, in kilograms, should be, respectively,
(A) 1.12 and 5.12.
(B) 2.68 and 12.28.
(C) 3.47 and 7.47.
(D) 5.00 and 10.76.
(E) 7.77 and 11.77.

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2016 enem__day2