1. 2.7 Mathematical Models Some will win, some will lose, some are born to sing the blues. Oh the movie never ends, it goes on and on and on and on. -Journey

2. Modeling Volume An open box with a square base is to be cut from a square piece of cardboard with side equal to 18 inches by cutting out a square from each corner and turning up the sides. 1) Write the volume V of the box as a function of the length x of the square cut from the box.

3. Modeling Area A farmer has 3000 feet of fencing to enclose a rectangular field. One side lies along a river, so only three sides need fencing. 1) Express the area A of the field enclosed by the fencing as a function of l, the length of the side parallel to the river.

4. Modeling Distance 1) Express the distance d from P to the origin as a function of x. 2. What is d if x = 0? 3. What is d if x = 1?

5. Modeling Area A rectangle is inscribed in a semicircle of radius 2. Let P = (x,y) be the point in Quadrant I that is a vertex of the rectangle and is on the circle. 1) Express the area A of the rectangle as a function of x.

6. Modeling Area A rectangle is inscribed in a semicircle of radius 2. Let P = (x,y) be the point in Quadrant I that is a vertex of the rectangle and is on the circle. 2) Express the perimeter P of the rectangle as a function of x. 2x2x

7. Modeling Area A) Express the area A of the rectangle as a function of x. B) What is the domain of A? C) Graph A=A(x)

8. Economics: Demand Equations In economics, revenue, R, in dollars, is defined as the amount of money received from the sale of a product and is equal to the Unit selling price p, in dollars, of the product times the number X of units actually sold. R = xp

9. Economics: R = xp The price p in dollars and the quantity x sold of a certain product obey the demand equation. 1. Express the revenue R as a function of x. 2. What is the revenue if 100 units are sold? 3.What quantity x maximizes revenue? What is the maximum revenue? 4. What price should the company charge to maximize revenue?

10. 2.7 Mathematical Models Some will win, some will lose, some are born to sing the blues. Oh the movie never ends, it goes on and on and on and on. -Journey Homework: p.134 #1, 3, 7a, 9abc, 11a, 15ab, 21 & 22