Question

Use technology to find the quadratic regression curve through the given points. (Round all coefficients to four decimal places.) (1, 4), (3, 7), (4, 5), (5, 3) y(x) = Crude oil imports to one country from another for 2009–2013 could be approximated by the following model where t is time in years since the start of 2000. I(t) = -33t^2 + 800t - 3,000 thousand barrels per day (9 ≤ t ≤ 13) According to the model, approximately when were oil imports to the country greatest? (Round your answer to two decimal places.) t = How many barrels per day were imported at that time? (Round your answer to two significant digits.) thousand barrels Revenue The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by q = -1.5p + 540 where q is the number of buggies it can sell in a month if the price is $p per buggy. At what price (in dollars) should it sell the buggies to get the largest revenue? p = $ What is the largest monthly revenue (in dollars)? $ Revenue Pack-Em-In has another development in the works. If it builds 40 houses in this development, it will be able to sell them at $260,000 each, but if it builds 70 houses, it will get only $230,000 each. Obtain a linear demand equation. (Let p be the price of a house and q the number of houses.) p(q) = Determine how many houses it should build to get the largest revenue. houses What is the largest possible revenue (in dollars)? $ The following table shows a tech product's sales during the financial years 2005–2009. (t is time in years since 2005.) Year t 0 1 2 3 4 iPod Sales S (millions) 22.8 39.4 51.2 54.8 54.7 (a) Find a quadratic regression model for these data. (Round coefficients to three significant digits.) S(t) = Graph the model together with the data. (b) What does the model predict for the product's sales in 2010, to the nearest million? $ million What does the model predict for the product's sales in 2011, to the nearest million? $ million The product's true sales in 2010 and 2011 were $50.4 million and $42.6 million respectively. Comment on your answers. - The answers we found are within $2 million of the actual sales, so the predictions were reasonably accurate. It is safe to extrapolate the model within two points of the given data. - The answers we found differ from the actual sales by more than $2 million, so the predictions were not reasonably accurate. This shows the danger of extrapolating the model beyond the given data. - The answers we found differ from the actual sales by more than $2 million, so the predictions were reasonably accurate. It is safe to extrapolate the model within two points of the given data. - The answers we found are within $2 million of the actual sales, so the predictions were not reasonably accurate. This shows the danger of extrapolating the model beyond the given data.

          Use technology to find the quadratic regression curve through the given points. (Round all coefficients to four decimal places.) (1, 4), (3, 7), (4, 5), (5, 3) y(x) = 

Crude oil imports to one country from another for 2009–2013 could be approximated by the following model where t is time in years since the start of 2000. I(t) = -33t^2 + 800t - 3,000 thousand barrels per day (9 ≤ t ≤ 13) According to the model, approximately when were oil imports to the country greatest? (Round your answer to two decimal places.) t = How many barrels per day were imported at that time? (Round your answer to two significant digits.) thousand barrels

Revenue The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by q = -1.5p + 540 where q is the number of buggies it can sell in a month if the price is $p per buggy. At what price (in dollars) should it sell the buggies to get the largest revenue? p = $ What is the largest monthly revenue (in dollars)? $

Revenue Pack-Em-In has another development in the works. If it builds 40 houses in this development, it will be able to sell them at $260,000 each, but if it builds 70 houses, it will get only $230,000 each. Obtain a linear demand equation. (Let p be the price of a house and q the number of houses.) p(q) = Determine how many houses it should build to get the largest revenue. houses What is the largest possible revenue (in dollars)? $

The following table shows a tech product's sales during the financial years 2005–2009. (t is time in years since 2005.) 
Year t 0 1 2 3 4 
iPod Sales S (millions) 22.8 39.4 51.2 54.8 54.7 
(a) Find a quadratic regression model for these data. (Round coefficients to three significant digits.) S(t) = 
Graph the model together with the data. 
(b) What does the model predict for the product's sales in 2010, to the nearest million? $ million 
What does the model predict for the product's sales in 2011, to the nearest million? $ million 
The product's true sales in 2010 and 2011 were $50.4 million and $42.6 million respectively. Comment on your answers. 
- The answers we found are within $2 million of the actual sales, so the predictions were reasonably accurate. It is safe to extrapolate the model within two points of the given data. 
- The answers we found differ from the actual sales by more than $2 million, so the predictions were not reasonably accurate. This shows the danger of extrapolating the model beyond the given data. 
- The answers we found differ from the actual sales by more than $2 million, so the predictions were reasonably accurate. It is safe to extrapolate the model within two points of the given data. 
- The answers we found are within $2 million of the actual sales, so the predictions were not reasonably accurate. This shows the danger of extrapolating the model beyond the given data.

Added by Joseph M.

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