Module 6: Interpreting Inputs and Outputs for Polynomial Functions Quiz

Step 1 of 1

The number of memberships at Sunrise Sky Spa since 2000 can be modeled by the function

m(t)=0.6t420t3+200t2500t+1000m(t)=0.6t420t3+200t2500t+1000,

wheretis the number of years since 2000.

[The graph plots Years since 2000 on the horizontal axis and Number of Memberships on the vertical axis. A curve falls from the second quadrant through (0, 1000) to (1.6, 600), and the rises to (9, 2050). From there, it falls to (14.6, 1350) and then rises through

Question 1 of 15

Question1

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Estimatem(5.5)m(5.5)and interpret its value in context.

The valuem(1500)5.5m(1500)5.5impliesthatthe company had approximately1,500memberships in mid-2005.

The valuem(5.5)1,600m(5.5)1,600impliesthatthe company had approximately1,600memberships in mid-2005.

The valuem(1600)5.5m(1600)5.5impliesthatthe company had approximately1,600memberships in mid-2005.

The valuem(5.5)1,500m(5.5)1,500impliesthatthe company had approximately1,500memberships in mid-2005.

A new online game,Salem Trial, was launched on January 1. The following is a scatter plot of the number of daily users on the first day of each month since January 1. A curve of best fit was found, with acoefficient of determinationr2=0.92r2=0.92.

[The curve f of x equals 14.06 x cubed minus 300.63 x squared plus 1762.59 x plus 243.96 rises through (0, negative 0.5) to (4, 3400), then falls to (10, 1900) and then rises through (13, 3500). A series of data points closely follow the curve and a data point is plotted well below the curve at (10, 1200). Text on the graph reads: r squared equals 0.92.

Question 2 of 15

Question2

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Use the regression function to estimate when the game attracted 2,000 online gamers.

The game had2,000gamers whenx 9andx 11.1, or on October1, and on a certain day in early December.

The game had2,000gamers whenx 1.2,x 9andx 11.1, or on a certain day in early February, on October 1, and on a certain day in early December.

Before this regression function is used to make a prediction, there is an outlier whent= 4that needs to be explained or removed from the data set.

Before this regression function is used to make a prediction, there is an outlier whent= 10 that needs to be explained or removed from the data set.

A new online game,Salem Trial, was launched on January 1. The following is a scatter plot of the number of daily users on the first day of each month since January 1. A curve of best fit was found, with acoefficient of determinationr2=92r2=92.

[The curve f of x equals 14.06 x cubed minus 300.63 x squared plus 1762.59 x plus 243.96 rises through (0, negative 0.5) to (4, 3400), then falls to (10, 1900) and then rises through (13, 3500). A series of data points closely follow the curve and a data point is plotted well below the curve at (10, 1200). Text on the graph reads: r squared equals 0.92.

Question 3 of 15

Question3

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Use the regression function to predict the number of online users on January 1 for the next year (whent= 12).

Before this regression function is used to make a prediction, there is an outlier whent= 10that needs to be explained or removed from the data set.

Before this regression function is used to make a prediction, there is an outlier whent= 4that needs to be explained or removed from the data set.

Sincef(2420)12f(2420)12, there will be approximately2,420online gamers on January1 for the next year.

Sincef(12)2,420f(12)2,420, there will be approximately2,420online gamers on January1 for the next year.

Question 4 of 15

Question4

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Traffic over a certain bridge every day, in number of vehicles per minute, can be modeled by the functionn(t)=2t3+40t2200t+350n(t)=2t3+40t2200t+350, wheretis the number of hours since8:00a.m.Find the number of vehicles per minutethat crossover the bridge at9:15a.m.every day.

Approximately281vehicles per minute go over the bridge at 9:15 a.m. every day.

Approximately159vehicles per minute go over the bridge at9:15a.m. every day.

Approximately2,584vehicles per minute go over the bridge at 9:15 a.m. every day.

Approximately195vehicles per minute go over the bridge at 9:15 a.m. every day.

Top Toys released two new toy planes. Plane 1 is simply launched into the air by hand and then falls onto the ground. Plane 2 has a motor and can fly upward. The following graph shows the height of those two planes, in feet, during a test.

[The curve p 1 of t begins at the origin, reaches its maximum at (6, 18), and ends at (12, 0). The curve p 2 of t begins at the origin, passes through the points (2.4, 21.5), (6, 14.8), (9.6, 21.6), and ends at (12, 0). The two curves intersect at (4.5, 17) and (7.4, 17).

Question 5 of 15

Question5

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Estimate the value ofp2(t)p2(t)whent= 8, and interpret its meaning in this context.

The point(8,18.4)implies that Plane 2 was approximately18.4ft. in the air for8seconds after it was launched.

The point(8,18.1)implies that Plane 2 was approximately8ft. in the air for18.1seconds after it was launched.

The point(8,18.1)implies that Plane 2 was approximately18.1ft. in the air for8seconds after it was launched.

The point(8,18.4)implies that Plane 2 was approximately8ft. in the air for18.4seconds after it was launched.

The following scatterplot shows Broadband Dish's customer satisfaction rate, in percentage,over the past year (wherex= 1 corresponds to January of last year). Apolynomialcurve of best fit is given with its equation and the correspondingcoefficient of determination.

[The parabola f of x equals 0.3081 x squared minus 4.3128 x plus 83.3414 begins at (0, 83), has a minimum at (7, 68) and ends at (14, 83). A series of data points closely approximate the parabola. Text on the graph reads: r squared equals 0.98.

Question 6 of 15

Question6

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Based on the regression function, when would the company'spredictedcustomer satisfaction rate reach80% in thisyear?

The company's customer satisfaction rate is predicted to reach 80% inMarchof this year.

The company's customer satisfaction rateis predicted toreach80%inJanuaryofthisyear.

The company's customer satisfaction rate will never reach80%thisyear.

The company's customer satisfaction rate is predicted to reach 80% in February of this year.

A new online game,Salem Trial, was launched on January 1. The following is a scatter plot of the number of daily users on the first day of each month since January 1. A curve of best fit was found, with acoefficient of determination ofr2=0.92r2=0.92.

[The curve f of x equals 14.06 x cubed minus 300.63 x squared plus 1762.59 x plus 243.96 rises through (0, negative 0.5) to (4, 3400), then falls to (10, 1900) and then rises through (13, 3500). A series of data points closely follow the curve and a data point is plotted well below the curve at (10, 1200). Text on the graph reads: r squared equals 0.92.]

Question 7 of 15

Question7

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Which statement is true about the outlier?

The effect of the outliercannotbe used to predictthe number of gamers on January 1 for the next year.

The outlier caused an underestimation of the number of gamers on January 1 for the next year.

The outlier caused an overestimation of the number of gamers on January 1 for the next year.

The outlier doesnotaffect the prediction of the number of gamers on January 1 for the next year.

Top Toys released two new toy planes. Plane 1 is simply launched by hand into the air and then falls onto the ground. Plane 2 has a motor and can fly upward. The following graph shows theheight of those two planes, in feet, during a test.

[The curve p 1 of t begins at the origin, reaches its maximum at (6, 18), and ends at (12, 0). The curve p 2 of t begins at the origin, passes through the points (2.4, 21.5), (6, 14.8), (9.6, 21.6), and ends at (12, 0). The two curves intersect at (4.5, 17) and (7.4, 17).

Question 8 of 15

Question8

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Estimate the value ofp2(t)p2(t)whent= 8. Write the answer in function notation.

p2(8)18.1p2(8)18.1

p2(8)18.4p2(8)18.4

Whent= 8,p2(t)p2(t)'s value is approximately 18.1.

(8, 18.4)

Top Toys released two new toy planes. Plane 1 is simply launched by hand into the air and then falls onto the ground. Plane 2 has a motor and can fly upward. The following graph shows theheight of those two planes, in feet, during a test.

[The curve p 1 of t begins at the origin, reaches its maximum at (6, 18), and ends at (12, 0). The curve p 2 of t begins at the origin, passes through the points (2.4, 21.5), (6, 14.8), (9.6, 21.6), and ends at (12, 0). The two curves intersect at (4.5, 17) and (7.4, 17).

Question 9 of 15

Question9

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Whent= 3, estimate the difference between those two functions' values.

Whent= 3, the difference between those two functions' values is approximately6.9.

Whent= 3, the difference between those two functions' values is approximately8.3.

Whent= 3, the difference between those two functions' values is approximately6.3.

Whent= 3, the difference between those two functions' values is approximately7.3.

Question 10 of 15

Question10

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Gas is getting more and more expensive.Sheais a student with a tight budget, so she wants the highest fuel efficiency from her car. This function,e(s)e(s), models her car's fuel efficiency in miles per gallon, depending ons, the car's speed in miles per hour. The function's equation is

e(s)=0.01s2+0.95s+9.1e(s)=0.01s2+0.95s+9.1.

Calculate the car's fuel efficiency when the car's speed is40miles per hour.

The car's fuel efficiency is40miles per gallon when the car's speed is31.1miles per hour.

The car's fuel efficiency is40miles per gallon when the car's speed is47.26miles per hour.

The car's fuel efficiency is31.1miles per gallon when the car's speed is40miles per hour.

The car's fuel efficiency is47.26miles per gallon when the car's speed is40miles per hour.

The number of memberships at Sunrise Sky Spa since 2000 can be modeled by the function

m(t)=0.6t420t3+200t2500t+1000m(t)=0.6t420t3+200t2500t+1000,

wheretis the number of years since 2000.

[The graph plots Years since 2000 on the horizontal axis and Number of Memberships on the vertical axis. A curve falls from the second quadrant through (0, 1000) to (1.6, 600), and the rises to (9, 2050). From there, it falls to (14.6, 1350) and then rises through

Question 11 of 15

Question11

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Estimate the solutionor solutionsfor theequationm(t)=2000m(t)=2000, and interpret its meaning in this context.

The solutionsaret7.8 andt 10.These solutions imply that the company had2,000memberships in late 2007 and at the beginning of 2010.

The solutionsaret8.25,t10, andt18.4.These solutions imply that the company had2,000memberships in late 2007, at the beginning of 2010, and in early 2016.

The solutionsaret7.8,t10, andt16.8.Thesesolutions imply that the company had2,000memberships in late 2007, at the beginning of 2010, and in late 2016.

Thesolutionist7.8. This solution implies that the company had2,000memberships in late 2007.

All Corners and Real Voice are cell phone service providers. Their customer satisfaction rates since 2000 are shown in the followinggraph.

[The graph plots Years since 2000 on the horizontal axis and Customer Satisfaction Rate on Percentage in the vertical axis. It shows two curves labeled Real Voice and All Corners. The curve labelled Real voice begins at (0, 64.5), reaches its minimum at (7, 45), and ends at (15, 70.5). The curve labelled All Corners begins at (0, 74), reaches its minimum at (9, 50), and ends at (15, 61). The two curves intersect at (10.9, 51).

Question 12 of 15

Question12

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To a customer, which cell phone company might seem like a better cell service provider in 2013?

All Cornersmight seem like a better cell service provider in 2013, since they had a customer satisfaction rate of about 62.5% compared to Real Voice's rate of 45.5% during at that time.

All Cornersmight seem like a better cell service provider in 2013, since they had a customer satisfaction rate of about 59.5% compared to Real Voice's rate of 54.5% during at that time.

Real Voicemight seem like a better cell service provider in 2013, since they had a customer satisfaction rate of about 59.5% compared to All Corners' rate of 54.5% during that time.

Real Voicemight seem like a better cell service provider in 2013, since they had a customer satisfaction rate of about 62.5% compared to All Corners' rate of 45.5% during at that time.

Top Toys released two new toy planes. Plane 1 is simply launched by hand into the air and then falls onto the ground. Plane 2 has a motor and can fly upward. The following graph shows theheight of those two planes, in feet, during a test.

[The curve p 1 of t begins at the origin, reaches its maximum at (6, 18), and ends at (12, 0). The curve p 2 of t begins at the origin, passes through the points (2.4, 21.5), (6, 14.8), (9.6, 21.6), and ends at (12, 0). The two curves intersect at (4.5, 17) and (7.4, 17).

Question 13 of 15

Question13

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Estimate those two planes' difference in height1second after the launch.

One second after they were launched, Plane 2 was approximately 10 feet higher than Plane 1.

One second after they were launched, Plane 1 was approximately 8.5feet higher than Plane 2.

One second after they were launched, Plane 2 was approximately 8.5feet higher than Plane 1.

One second after they were launched, Plane 1 was approximately 10feet higher than Plane 2.

Question 14 of 15

Question14

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The number of memberships at Sunrise Sky Spa since 2000 can be modeled by the function

m(t)=0.6t420t3+200t2500t+1000m(t)=0.6t420t3+200t2500t+1000,

wheretis the number of years since 2000. Calculate the number of memberships on January 1, 2005.

There were approximately 1,221memberships on January 1, 2005.

There were approximately 1,375memberships on January 1, 2005.

There were approximately 1,693memberships on January 1, 2005.

There were approximately903memberships on January 1, 2005.

The number of memberships at Sunrise Sky Spa since 2000 can be modeled by the function

m(t)=0.6t420t3+200t2500t+1000m(t)=0.6t420t3+200t2500t+1000,

wheretis the number of years since 2000.

[The graph plots Years since 2000 on the horizontal axis and Number of Memberships on the vertical axis. A curve falls from the second quadrant through (0, 1000) to (1.6, 600), and the rises to (9, 2050). From there, it falls to (14.6, 1350) and then rises through

Question 15 of 15

Question15

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Estimate the solutionor solutionsfor theequationm(t)=3000m(t)=3000, and interpret its meaning in this context.

The solutionist20t20. This solution implies that the company had3,000memberships by 2020.

The solutionsaret= 10andt17.9t17.9.Thesesolutions imply that the company had3,000memberships at the beginning of 2010 and in late 2017.

The solutionist17.9t17.9.This solution implies that the company had3,000memberships in late 2017.

The solutionsaret= 0andt17.9t17.9.These solutions imply that the company had3,000memberships at the beginning of 2000 and in late 2017.