assets.openstudy.comassets.openstudy.com/updates/attachments/55fd7ca7e4b0027... · Web view(04.07) The same amount of trash from a landfill is recycled every day. The function below

Question 1 (Multiple Choice Worth 1 points)

(04.01)Which of the following shows the correct steps to find

the value of ?


(04.06)The sales totals at Robert's food store have increased linearly over the months. Which of these best shows the sales in the first three months?$1200 in the first month, $1212 in the second month, $1224.12 in the third month$1200 in the first month, $1236 in the second month, $1273.08 in the third month$1200 in the first month, $1285.48 in the second month, $1370.96 in the third month$1200 in the first month, $1224.28 in the second month, and $1248.48 in the third month


(04.02)What is the exact value of the expression − + ? Simplify if possible.

2268


(04.05)The number of subscribers y to a newspaper after t years is shown by the equation below:y = 75(0.95)tWhich conclusion is correct about the number of subscribers to the newspaper?It increased by 75% every year.It decreased by 75% every year.It increased by 5% every year.It decreased by 5% every year.


(04.01)Simplify .


(04.07)The functions f(x) and g(x) in the table below show Jane's and Mariah's savings respectively, in dollars, after x days. Some values are missing in the table.x(years) 1 2 3f(x) = 2xJane's savings in dollars

2 4

g(x) = 2xMariah's savings in dollars

2 4

Which statement best describes Jane and Mariah's savings in the long run?

Jane will save more than Mariah.Mariah will save more than Jane.The savings will increase by the same factor for both.The savings will increase by the same percentage for both.


(04.03)Diana invested some money in a bank at a fixed rate of interest compounded annually. The equation below shows the value of her investment after x years:f(x) = 400(1.01)xWhat was the average rate of change of the value of Diana's investment from the second year to the fifth year?1.01 dollars per year2.47 dollars per year4.12 dollars per year12.36 dollars per year


(04.05)The table below shows the functions to represent the sale f(t), in thousands, of four companies in t years:Company A B C D

Sale f(t) = 1.05t

f(t) = 0.75t

f(t) = 1.212t

f(t) = 0.9712t

Which of the following companies showed an exponential decay in sale?

Company A and Company CCompany B and Company DCompany C and Company DCompany A and Company B


(04.01)Which of the following is equal to ?


(04.05)The price of gold has increased by 35% per year from 2000. In the year 2000, Harry bought a gold ring for $590. Which of the following functions f(x) can be used to

represent the price of the ring x years after 2000?f(x) = 590(1.35)xf(x) = 590(0.65)xf(x) = 35(0.41)xf(x) = 35(1.59)x


(04.07)The functions p(x) and g(x) are shown below:g(x) = 0.09xp(x) = (0.09)xWhich statement best describes the graph of p(x) and g(x)?The graphs will both have their y-intercept equal to 1.The graphs will both have their y-intercept equal to 0.09.The graph of p(x) will eventually exceed the graph of g(x).The graph of g(x) will eventually exceed the graph of p(x).


(04.01)Which of the following best defines ?Square root of 9Cube root of 9Cube root of 3Square root of 3


(04.05)The number of members f(x) in a local swimming club increased by 30% every year over a period of x years. The function below shows the relationship between f(x) and x:f(x) = 10(1.3)xWhich of the following graphs best represents the function?


(04.03)A music competition on television had five elimination rounds. After each elimination, only half of the contestants were sent to the next round. The table below shows the number of contestants in each round of the competition:x 1 2 3 4 5f(x)

64

32

16 8 4

Compute the average rate of change of f(x) from x = 3 to x = 5 and describe what it represents.

−6 contestants per round, and it represents the number of contestants who will reach the final round−28 contestants per round, and it represents the number of contestants who will reach the final round−6 contestants per round, and it represents the average rate at which the number of contestants decreased from the third round to the fifth round−28 contestants per round, and it represents the average rate at which the number of contestants decreased from the third round to the fifth round


(04.03)The function f(x) = 800(1.09)5x shows the growth due to interest that Jim earns on an investment.The steps to calculate an equivalent function are shown below:

[Ste f(x) =

p 1] 800(1.09)5x

[Step 2]

f(x) = 800(1.095)5x

[Step 3]

f(x) = 800(1.5386)5x

[Step 4]

f(x) = 800(1.5386)x

Which of the following is the first incorrect step?

Step 1Step 2Step 3Step 4


(04.06)Sasha and Mona practiced swimming every day. They increased the number of minutes of swimming every week as described below:Sasha: Practiced swimming for 10 minutes every day in the first week, 20 minutes in the second week, 40 minutes in the third week, and 80 minutes in the fourth week.Mona: Practiced swimming for 10 minutes every day in the first week, 20 minutes in the second week, 30 minutes in the third week, and 40 minutes in the fourth week.Which statement best describes the methods used by Sasha and Mona to increase the time they practiced swimming?Mona's method is linear because the number of minutes increased by an equal factor every week.Sasha's method is exponential because it increases by an equal number every week.Mona's method is exponential because it increases by a fixed factor, and Sasha's method is linear because it

increases by a fixed number.Sasha's method is exponential because it increases by a fixed factor, and Mona's method is linear because it increases by a fixed number.


(04.05)The graph of f(x) = 2x + 3 shifts 10 units to the right when it is replaced with the graph of f(x) = 2x − k. What is the value of k?371013


(04.05)Maureen is taking an antibiotic. The table below shows the amount of antibiotic f(t), in mg, that was present in her body after time t:t (hours)

1 2 3 4 5

f(t) (mg)

150

90

54

32.4

19.4

Ken was administered 200 mg of the same antibiotic. The amount of antibiotic f(t) in his body after time t is shown by the equation below:

f(t) = 200(0.976)t

Which statement best describes the rate at which Maureen's

and Ken's bodies eliminated the antibiotic?

Maureen's body eliminated the antibiotic faster than Ken's body.Maureen's body eliminated the antibiotic at the same rate as Ken's body.Maureen's body eliminated the antibiotic at half of the rate at which Ken's body eliminated the antibiotic.Maureen's body eliminated the antibiotic at one-fourth of the rate at which Ken's body eliminated the antibiotic.


(04.05)The population f(x), in millions, of State A of a country after x years is represented by the function shown below:f(x) = 4(1.08)xThe graph shows the population g(x), in millions, of State B of the country after x years:

Which conclusion is correct about the population of State A and State B?The original population of State A was double of the original

population of State B.The original population of State B was double of the original population of State A.The original population of State A was four times of the original population of State B.The original population of State A was equal to the original population of State B.


(04.07)The amount of radioactive uranium changes with time. The table below shows the amount of radioactive uranium f(t) left after time t:

t(hours) 0

0.5

1

f(t)100

50

25

Which exponential function best represents the relationship between f(t) and t?

f(t) = 100(0.25)tf(t) = 0.25(100)tf(t) = 100 (0.5)tf(t) = 0.25(50)t


(04.03)Jane is studying the rate at which the sale of a particular brand of chocolate has increased over the years. The graph below shows the number of bars sold y, in thousands, after x years since the year 2000:

What does the y-intercept of the graph represent?Price of a bar of chocolateNumber of bars sold in 2000Number of bars sold before 2000Rate of increase in the sale of chocolates


(04.07)A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce:f(n) = 9(0.7)nWhat does the number 9 in the function represent?Number of times the ball was dropped.Height from which the ball was dropped.Height to which the ball will bounce at the nth bounce.Number of times the ball bounces at the nth bounce.


(04.03)The number of users of the internet in a town increased by a factor of 1.01 every year from 2000 to 2010. The function below shows the number of internet users f(x) after x years from the year 2000:f(x) = 3000(1.01)xWhich of the following is a reasonable domain for the function?0 ≤ x ≤ 102000 ≤ x ≤ 20100 ≤ x ≤ 3000All positive integers


(04.06)Chang added some chlorine to the water in a pool. The chlorine evaporated at a fixed rate every week. The table below shows the amount of chlorine f(n), in ounces, that was left in the pool after n weeks:

nf(n)

1 24

2 12

3 64 3

Which function best shows the relationship between n and f(n)?

f(n) = 48(0.5)n−1

f(n) = 24(0.5)nf(n) = 24(0.5)n−1f(n) = 48(0.5)n+1


(04.05)The graphs below show four functions:

Which graph best shows the function f(x) = 5(2)−x to represent the rate at which a radioactive substance decays?Graph AGraph BGraph CGraph D


(04.05)Which statement best describes the effect of

replacing the function f(x) = 2x − 2 with the function g(x) = 2x + 3?The graph shifts 1 units left.The graph shifts 5 units left.The graph shifts 1 unit right.The graph shifts 3 units right.


(04.07)The same amount of trash from a landfill is recycled every day. The function below shows the total number of tons of trash n left in the landfill after x days. Assume that new trash is not added to the landfill.n = 50000 − 1000xWhat does the number 1000 represent?Amount of trash left after 1 dayAmount of trash recycled in x daysAmount of trash recycled every dayAmount of trash originally in the landfill


(04.05)The average annual salary of the employees of a company in the year 2005 was ninety thousand dollars. It increased by the same factor each year and in 2006, the average annual salary was $91,200. Let f(x) represent the average annual salary, in thousand dollars, after x years since 2005. Which of the following best represents the relationship between x and f(x)?f(x) = 91.2(1.013)xf(x) = 90(1.013)xf(x) = 91.2(2.2)xf(x) = 90(2.2)x


(04.02)An expression is shown below: Which statement is true about the expression?It is rational and equal to 3.It is rational and equal to 4.It is irrational and equal to .It is irrational and equal to .


(04.03)Jake forgot to replace the cap on a bottle of cologne. The cologne began to evaporate at the rate of 18% per day. If the original amount of cologne in the bottle was 50 grams, which of the following graphs best represents the amount of cologne f(x) remaining in the bottle after x days?


(04.03)The graph below shows three functions:

Which function has all real numbers as its domain?Only f(x)Both g(x) and p(x)Both f(x) and g(x)Only p(x)


(04.06)A store had 235 MP3 players in the month of January. Every month, 30% of the MP3 players were sold and 50 new MP3 players were stocked in the store.Which recursive function best represents the number of MP3 players in the store f(n) after n months?f(n) = 0.7 × f(n − 1) + 50, f(0) = 235, n > 0f(n) = 237 − 0.7 × f(n − 1) + 50, f(0) = 235, n > 0f(n) = 0.3 × f(n − 1) + 50, f(0) = 235, n > 0f(n) = 237 + 0.7 × f(n − 1) + 50, f(0) = 235, n > 0


(04.03)Which of the following is an equivalent function to the function below?f(x) = 40(1.04)4xf(x) = 40(4.1600)xf(x) = 480(1.04)xf(x) = 40(1.1699)xf(x) = 480(4.1600)x

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