assets.openstudy.comassets.openstudy.com/updates/attachments/55f49bc5e4b... · web viewthe number...

The number of members f(x) in Joe's health club increased by 25% every year over a period of x years. The function below shows the relationship between f(x) and x:f(x) = 15(1.25)xWhich of the following graphs best represents the function?

Question 2 (Multiple Choice Worth 1 points)

(04.06)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?f(n) = 175 − 0.9 × f(n − 1) + 10, f(0) = 175, n > 0f(n) = 0.1 × f(n − 1) + 10, f(0) = 175, n > 0f(n) = 175 + 0.9 × f(n − 1) + 10, f(0) = 175, n > 0f(n) = 0.9 × f(n − 1) + 10, f(0) = 175, n > 0


(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)


(04.05)The average annual salary of the employees of a company in the year 2005 was $80,000. It increased by the same factor each year and in 2006, the average annual salary was $88,000. 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)?f(x) = 88(0.88)xf(x) = 88(1.1)xf(x) = 80(0.88)xf(x) = 80(1.1)x


(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 .


(04.02)What is the exact value of the expression − + ? Simplify if possible.812

812


(04.05)The price of bronze has increased by 10% per year from 2000. In the year 2000, Harry bought a bronze medal for $120. Which of the following functions f(x) can be used to represent the price of the medal x years after 2000?f(x) = 120(0.9)xf(x) = 10(120)xf(x) = 120(1.1)xf(x) = 10(1.1)x


(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 function f(x) = 800(1.09)4x shows the growth due to interest that Jim earns on an investment.The steps to calculate an equivalent function are shown below:[Step 1]

f(x) = 800(1.09)4x

[Step 2]

f(x) = 800(1.094)x

[Step 3]

f(x) = 800(1.4116)x

[Step 4]

f(x) = (1129.27)x

Which of the following is the first incorrect step?

Step 1Step 2Step 3Step 4


(04.07)The functions f(x) and g(x) are shown below:f(x) = 0.05xg(x) = (0.05)xWhich statement best describes the graph of f(x) and g(x)?The graph of g(x) will eventually exceed the graph of f(x).The graph of f(x) will eventually exceed the graph of g(x).The graphs will both have their y-intercept equal to 1.The graphs will both have their y-intercept equal to 0.05


(04.03)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?6.43 dollars per year8.24 dollars per year12.86 dollars per year14.26 dollars per year


(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 unit left.The graph shifts 5 units left.The graph shifts 5 units right.The graph shifts 1 unit right.


(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


(04.03)Which of the following is an equivalent function to the function below?f(x) = 50(1.05)12xf(x) = 50(1.7959)xf(x) = 50(12.6000)xf(x) = 600(1.05)xf(x) = 4.2(1.05)x


(04.06)Bruce 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)

1 542 27

3 13.5

4 6.75

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

f(n) = 108(0.5)n−1f(n) = 54(0.5)nf(n) = 108(0.5)n+1f(n) = 54(0.5)n−1


(04.03)A dance competition on television had five elimination rounds. After each elimination, only one-fourth 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)

512

128

32 8 2

Compute the average rate of change of f(x) from x = 2 to x = 4 and describe what it represents.

−60 contestants per round, and it represents the average rate at which the number of contestants changed from the second round to the fourth round−120 contestants per round, and it represents the average rate at which the number of contestants changed from the second round to the fourth round−60 contestants per round, and it represents the number of contestants who will reach the final round−120 contestants per round, and it represents the number of contestants who will reach the final round


(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 .


(04.05)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?Graph AGraph BGraph CGraph D


(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 ?


(04.01)Which of the following best defines ?Cube root of 4Square root of 4

Cube root of 2Square root of 2


(04.06)The sales totals at Linda's food store have increased exponentially over the months. Which of these best shows the sales in the first three months?$1200 in the first month, $1260 in the second month, and $1323 in the third month$1200 in the first month, $1250 in the second month, $1300 in the third month$1200 in the first month, $1272 in the second month, $1344 in the third month$1200 in the first month, $1285 in the second month, $1370 in the third month


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

3 9

f(x) = 3x + 5Ben's savings in

8 11

dollars

Which statement best describes Kim and Ben's savings in the long run?

The savings will increase by the same factor for both.The savings will increase by the same amount for both.Kim will save more than Ben.Ben will save more than Kim.


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

the value of ?


(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 day

Amount of trash recycled in x daysAmount of trash recycled every dayAmount of trash originally in the landfill


(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)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.


(04.06)Scott and Harry went cycling every day. They increased the number of minutes of cycling every week as described below:Scott: Cycled for 10 minutes every day in the first week, 15 minutes in the second week, 20 minutes in the third week, and 25 minutes in the fourth week.Harry: Cycled 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.Which statement best describes the methods used by Scott and Harry to increase the time they spent cycling?Scott's method is linear because the number of minutes increased by an equal number every week.Harry's method is linear because the number of minutes increased by an equal factor every week.Both Harry's and Scott's method is exponential because the number of minutes increased by an equal factor every week.Both Harry's and Scott's method is exponential because the number of minutes increased by an equal number every week.


(04.07)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?

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


(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 graph of f(x) = 2x + 4 shifts six units to the right when it is replaced with the graph of f(x) = 2x − k. What is the value of k?24610

assets.openstudy.comassets.openstudy.com/updates/attachments/55f49bc5e4b... · web viewthe number...

Documents