1) Each year, a baseball team sells boxes of chocolates as a fundraiser to lower the cost of team fees. The price of the chocolates and the number of boxes sold varies each year. The information from five years of sales is given in the table below.
|
Price per box ($)
|
3.00
|
4.00
|
5.50
|
6.50
|
8.00
|
|
Boxes sold
|
5303
|
3360
|
1777
|
1316
|
1019
|
a. Find the regression equation in the form y=ax2 +bx2 +cx +d that best approximates the data. Express the values of a, b, c, and d to the nearest hundredth.
b. Use the equation to find the number of boxes, to the nearest whole number, that the team will sell if they charge $4.35 per box.
c. One year, the team only sold 125 boxes of chocolates. What price did they charge for each box?
d. If the team raises the price too high, they will not sell any boxes. Use your regression equation to predict the price of a box that will result in zero boxes sold.
2) The path of a baseball after it is hit is modelled by the equation h= -4.98t2 +12.51t +1.36, where h is the height, in metres, of the ball and t is the time, in seconds, after the ball is hit.
a. Find the maximum height that the ball reaches, to the nearest hundredth of a metre.
b. Determine the height of the ball, to the nearest hundredth of a metre, at 2.5 seconds.
c. Determine when the ball is at a height of 8m, to the nearest hundredth of a second.
d. State the y-intercept of the graph to the nearest hundredth. Describe what the y-intercept represents in the context of this question.
e. i. Find the coordinates of both x-intercepts of the graph to the nearest hundredth.
ii. State what the positive x-intercept represents in the context of this problem.
iii. Explain why the negative x-intercept is not valid in the context of this problem.