04.08 Module Four Review and Practice Note: It is recommended that you save your response as you complete each question. Question 1 (1 point)Which of the following best defines ? (1 point)Question 1...

04.08 Module Four Review and Practice

Note: It is recommended that you save your response as you complete each question.

Question 1 (1 point)Which of the following best defines ? (1 point)Question 1 options:

1) Cube root of 4

2) Square root of 4

3) Cube root of 2

4) Square root of 2

Save Question 2 (1 point)Which of the following shows the correct steps to find the value of ? (1 point)Question 2 options:

1)

2)

3)

4)

Save Question 3 (1 point)Simplify (1 point)Question 3 options:

1)

2)

3)

4)

Save Question 4 (1 point)Which of the following is equal to ? (1 point)Question 4 options:

1)

2)

3)

4)

Save Question 5 (1 point)What is the exact value of the expression - + ? Simplify if possible. (1 point)Question 5 options:

1) 8

2) 12

3) 8

4) 12

Save Question 6 (1 point)An expression is shown below:Which statement is true about the expression? (1 point)Question 6 options:

1) It is rational and equal to 4.

2) It is rational and equal to 5.

3) It is irrational and equal to .

4) It is irrational and equal to .

Save Question 7 (1 point)The expression below shows the population of butterflies in a forest after 4x years:f(x) = 40(1.04)4xWhich of the following is an equivalent function? (1 point)Question 7 options:

1) f(x) = 40(4.1600)x

2) f(x) = 480(1.04)x

3) f(x) = 40(1.1699)x

4) f(x) = 480(4.1600)x

Save Question 8 (1 point)The function f(x) = 800(1.09)4xshows the growth due to interest that Jim earns on an investment.The steps to calculate an equivalent function are shown below:

f(x) = 800(1.09)4x	[Step 1]
f(x) = 800(1.094)x	[Step 2]
f(x) = 800(1.4116)x	[Step 3]
f(x) = (1129.27)x	[Step 4]

Which of the following is the first incorrect step? (1 point)Question 8 options:

1) Step 1

2) Step 2

3) Step 3

4) Step 4

Save Question 9 (1 point)Zen deposited some money in a savings account. The graph below shows the value of Zen's investment y, in dollars, after x months:What does the y intercept of the graph represent? (1 point)Question 9 options:

1) Rate of interest offered to Zen

2) Final value of Zen's investment

3) Total number of months for which Zen invested the money

4) Amount of money Zen deposited in the savings account

Save Question 10 (1 point)Jake forgot to replace the cap on a bottle of deodorant. The deodorant began to evaporate at the rate of 12% per day. If the original amount of deodorant in the bottle was 30 grams, which of the following graphs best represents the amount of deodorant f(x) that would remain in the bottle after x days? (1 point)Question 10 options:

1)

2)

3)

4)

Save Question 11 (1 point)The number of bacteria in a sample increased by a factor of 2 every minute from 9:05 AM to 9:55 AM. The function below shows the number of bacteria in the sample f(x) after x minutes from 9:05 AM:f(x) = 10(2)xWhich of the following is a reasonable domain for the function? (1 point)Question 11 options:

1) 0 = x = 10

2) 5 = x = 55

3) 0 = x = 50

4) All positive integers

Save Question 12 (1 point)The graph below shows three functions:Which function has all real numbers as its domain? (1 point)Question 12 options:

1) Only f(x)

2) Both g(x) and p(x)

3) Both f(x) and g(x)

4) Only p(x)

Save Question 13 (1 point)Jack invested some money in a bank at a fixed rate of interest compounded annually. The equation below shows the value of his investment after x years:f(x) = 300(1.02)xWhat was the average rate of change of the value of Jack's investment from the third year to the fifth year? (1 point)Question 13 options:

1) 6.43 dollars per year

2) 8.24 dollars per year

3) 12.86 dollars per year

4) 14.26 dollars per year

Save Question 14 (1 point)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	5
f(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.(1 point)Question 14 options:

1) -6 contestants per round, and it represents the number of contestants who will reach the final round

2) -28 contestants per round, and it represents the number of contestants who will reach the final round

3) -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

4) -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

Save Question 15 (1 point)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? (1 point)Question 15 options:

1)

2)

3)

4)

Save Question 16 (1 point)The graphs below show four functions:Which graph best shows the function f(x) = 3(3)-x to represent the rate at which a radioactive substance decays? (1 point)Question 16 options:

1) Graph A

2) Graph B

3) Graph C

4) Graph D

Save Question 17 (1 point)The number of subscribers y to a magazine after t years is shown by the equation below:y = 95(0.75)tWhich conclusion is correct about the number of subscribers to the magazine? (1 point)Question 17 options:

1) It increased by 25% every year.

2) It decreased by 25% every year.

3) It increased by 75% every year.

4) It decreased by 75% every year.

Save Question 18 (1 point)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? (1 point)Question 18 options:

1) Company A and Company C

2) Company B and Company D

3) Company C and Company D

4) Company A and Company B

Save Question 19 (1 point)The population f(x), in millions, of State A of a country after x years is represented by the function shown below:f(x) = (1.08)tThe 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? (1 point)Question 19 options:

1) The original population of State B was half of the original population of State A.

2) The original population of State A was half of the original population of State B.

3) The original population of State B was one-fourth of the original population of State A.

4) The original population of State A was one-fourth of the original population of State B.

Save Question 20 (1 point)Henry is taking a medicine for a common cold. His body metabolizes the medicine over a certain time interval. The table below shows the amount of medicine f(t), in mg, that was present in Henry's body after time t.

t (hours)	1	2	3	4	5
f(t) (mg)	282	265.08	249.18	234.22	220.17

Greg was administered 200 mg of the same medicine. The amount of medicine in his body f(t) after time t is shown by the equation below.f(t) = 200(0.88)tWhich statement best describes the rate at which Henry and Greg's bodies eliminated the medicine? (1 point)Question 20 options:

1) Henry's body eliminated the antibiotic faster than Greg's body.

2) Henry's body eliminated the antibiotic at the same rate as Greg's body.

3) Henry's body eliminated the antibiotic at half of the rate at which Greg's body eliminated the antibiotic.

4) Henry's body eliminated the antibiotic at one-fourth of the rate at which Greg's body eliminated the antibiotic.

Save Question 21 (1 point)The price of silver has increased by 15% per year from 2000. In the year 2000, Harry bought a silver bowl for $190. Which of the following functions f(x) can be used to represent the price of the bowl x years after 2000? (1 point)Question 21 options:

1) f(x) = 190(0.85)x

2) f(x) = 190(1.15)x

3) f(x) = 15(190)x

4) f(x) = 15(0.85)x

Save Question 22 (1 point)The average annual salary of the employees of a company in the year 2005 was $70,000. It increased by the same factor each year and in 2006, the average annual salary was $82,000. 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)? (1 point)Question 22 options:

1) f(x) = 70(1.17)x

2) f(x) = 82(1.17)x

3) f(x) = 70(2.2)x

4) f(x) = 82(2.2)x

Save Question 23 (1 point)Which statement best describes the effect of replacing the function f(x) = 2x + 2 with the function g(x) = 2x - 3? (1 point)Question 23 options:

1) The graph shifts 1 unit left.

2) The graph shifts 5 units left.

3) The graph shifts 5 units right.

4) The graph shifts 1 unit right.

Save Question 24 (1 point)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? (1 point)Question 24 options:

1) 3

2) 7

3) 10

4) 13

Save Question 25 (1 point)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? (1 point)Question 25 options:

1) Mona's method is linear because the number of minutes increased by an equal factor every week.

2) Sasha's method is exponential because it increases by an equal number every week.

3) 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.

4) 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.

Save Question 26 (1 point)The sales totals at Robert's food store have increased linearly over the month. Which of these best shows the sales in the first three months? (1 point)Question 26 options:

1) $1200 in the first month, $1212 in the second month, $1224.12 in the third month

2) $1200 in the first month, $1236 in the second month, $1273.08 in the third month

3) $1200 in the first month, $1285.48 in the second month, $1370.96 in the third month

4) $1200 in the first month, $1224.28 in the second month, and $1248.48 in the third month

Save Question 27 (1 point)A store had 175 cell phones in the month of January. Every month, 10% of the cell phones were sold and 10 new cell phones were stocked in the store.Which recursive function best represents the number of cell phones in the store f(n) after n months? (1 point)Question 27 options:

1) f(n) = 175 - 0.9 × f(n - 1) + 10, f(0) = 175, n > 0

2) f(n) = 0.1 × f(n - 1) + 10, f(0) = 175, n > 0

3) f(n) = 175 + 0.9 × f(n - 1) + 10, f(0) = 175, n > 0

4) f(n) = 0.9 × f(n - 1) + 10, f(0) = 175, n > 0

Save Question 28 (1 point)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:

n	f(n)
1	24
2	12
3	6
4	3

Which function best shows the relationship between n and f(n)? (1 point)Question 28 options:

1) f(n) = 48(0.5)n-1

2) f(n) = 24(0.5)n

3) f(n) = 24(0.5)n-1

4) f(n) = 48(0.5)n+1

Save Question 29 (1 point)The amount of a radioactive material changes with time. The table below shows the amount of radioactive material f(t) left after time t:

t(hours)	0	1	2
f(t)	100	50	25

Which exponential function best represents the relationship between f(t) and t? (1 point)Question 29 options:

1) f(t) = 0.5(100)t

2) f(t) = 100 (0.25)t

3) f(t) = 0.25(50)t

4) f(t) = 100(0.5)t

Save Question 30 (1 point)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	3
f(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? (1 point)Question 30 options:

1) Jane will save more than Mariah.

2) Mariah will save more than Jane.

3) The savings will increase by the same factor for both.

4) The savings will increase by the same percentage for both.

Save Question 31 (1 point)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)? (1 point)Question 31 options:

1) The graphs will both have their y-intercept equal to 1.

2) The graphs will both have their y-intercept equal to 0.09.

3) The graph of p(x) will eventually exceed the graph of g(x).

4) The graph of g(x) will eventually exceed the graph of p(x).

Save Question 32 (1 point)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? (1 point)Question 32 options:

1) Amount of trash left after 1 day

2) Amount of trash recycled in x days

3) Amount of trash recycled every day

4) Amount of trash originally in the landfill

Save Question 33 (1 point)A fuel is purified by passing it through a clay pipe. Each foot of the clay pipe removes a fixed percentage of impurities in the fuel. Let f(x) represent the amount of pollutants, in tons, left in the fuel after it had passed through x feet of the clay pipe.f(x) = 10(0.8)xWhat does the number 0.8 represent? (1 point)Question 33 options:

1) Every foot of the pipe removes 20% of the pollutant.

2) Every foot of the pipe removes 80% of the pollutant.

3) The original amount of pollutant present in the fuel was 80 tons.

4) The original amount of pollutant present in the fuel was 20 tons.

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