Math SLP Homework

SLP

1. A company’s costs, in millions of dollars, are given by the equation, C = x2 – 3x – 27, where x is the number of items sold, in thousands. What are the costs when 1,000 items are sold? 1,500 items? (Hint: If the number of items sold is 1000, then x=1.)

2. A company’s costs, in millions of dollars, are given by the equation, C = x2 – 3x – 27, where x is the number of items sold, in thousands. How many items must be sold for the costs to be zero?

3. An object’s height, in meters, when thrown vertically from the ground at a velocity of 80 m/s is given by the equation H = -4.9t2 + 80t. Ignoring wind resistance, what is the height of the ball after 2 seconds? 3 seconds? 10 seconds?

4. An object’s height, in meters, when thrown vertically from the ground at a velocity of 80 m/s is given by the equation H = -4.9t2 + 80t. Ignoring wind resistance, how many seconds will it take the object to return to the ground? In other words, when is H = 0?

5. The distance d traveled by an object during t seconds, when starting with velocity v and subjected to an acceleration a, is given by the equation d = (0.5)at2 + vt. A missile traveling with an initial velocity of 100 m/s fires its rocket motor for 5 seconds. During that period, it experiences an acceleration of 50 m/s2. How far does it travel during the five seconds the motor is firing?

Use the following information for problems 6 through 10.

Gatorade/Tropicana North America, a subsidiary of PepsiCo, produces fruit juices and other flavored beverages. Based on data from 1999 to 2001, the net sales (revenue) of Gatorade/Tropicana North America may be modeled by
R(t) = -107t2+496t+3452 million dollars
and the operating profit (earnings before interest and taxes) may be modeled by
P(t) = −18.5t2 + 85.5t + 433 million dollars

– where t is the number of years since 1999. (Source: Modeled from 2001 PepsiCo Annual Report, p.44.)

6. Profit = Revenue – Costs. Find an expression representing the costs for this time period.

7. What was the revenue in 2000? (Years since 1999 = 1.)

8. What was the profit in 2000?

9. Use the equation found in question 6 to find the costs in 2000.

10. R and P were calculated in problems 7 and 8. Use these results to find C. How does this value compare with the result of problem 9?