5. A particular rocket taking off from the Earth's surface uses fuel at a constant rate of 12.5 gallons per minute. The rocket initially contains 225 gallons of fuel. (a) Determine a linear model, in y= ax+b_form, (b) Below is a general sketch of what the graph of your model should look like. Using your calculator, determine the x and y intercepts of this model and label them on the graph at points A and B respectively. for the amount of fuel the rocket has remaining, y, as a function of the number of minutes, x. (c) The rocket must still contain 50 gallons of fuel when it hits the stratosphere. What is the maximum number of minutes the rocket can take to hit the stratosphere? Show this point on your graph by also graphing the horizontal line y= 50 and showing the intersection point.

Find the equation of the parabola, y = ax2+bx+c, that passes through the points (−1, 6), (1, 4), and (2, 9). [Hint: For each point, give a linear equation in a, b, and c.]

Now find a single equation that is perpendicular to all of these lines (do not use the y-axis). Can you graph your equation using the calculator? Mocels Lab Exercise 4 Recycling Over time, according to records kept by the Environmental Protection Agency (found at www.epa.gov), recycling rates have increased from 10% of municipal solid waste generated in 1980 to 16% in 1990, to 29% in 2000, and to 34% in 2009. Meanwhile, disposal of waste to a landfill has decreased from 89% of the amount generated in 1980 to 54.3% of solid waste in 2009. The prediction equation (or least- squares prediction equation) for the percent of solid waste recycled by Americans is y = 0.932x -1837 where y = percent of solid waste recycled and x is the year. (a) Graph these data (percent recycled vs. year), leaving room at both ends for past and future years. Draw the line given by the prediction equation on your graph also. (b) Is the slope positive or negative? What does the slope tell us about the rate of…