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1.6a Modeling with Functions!!!

In this section, we focus on using functions to model real-world situations. Learn how to write algebraic expressions and quantities as functions, including examples involving numbers, circles, triangles, costs, profit, and more.

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1.6a Modeling with Functions!!!

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  1. 1.6a Modeling withFunctions!!! The last section of the chapter!!!

  2. Recall… One of the main themes of Sec. 1.1 was to model real-world situations in several different ways (e.g., numerically, graphically, etc.). We focus now on using functions in models. Of course, our first task is to become experts at writing these functions…

  3. Consider these problems… Write an algebraic expression for the quantity described: A number x increased by 5 and then tripled. Four more than 5% of a number x.

  4. Guided Practice Write the area of a circle as a function of its: (a) radius r (b) diameter d (c) circumference C

  5. Guided Practice Write an algebraic expression for the quantity described: The area of a triangle whose altitude is 2 more than its base length x. Income after a 3% drop in the current income of x dollars.

  6. Guided Practice Choose a variable and write a mathematical expression for the quantity described verbally: Total Cost: The total cost is $28,000 increased by 9% plus $19.85 for each item produced. Let C be the total cost and n be the number of items produced

  7. Guided Practice Choose a variable and write a mathematical expression for the quantity described verbally: Profit: The profit consists of a franchise fee of $200,000 plus 12% of all sales. Let P be the profit and s be the amount of sales

  8. Guided Practice Write the specified quantity as a function of the specified variable. In some cases, it may be helpful to draw a picture. One leg of a right triangle is twice as long as the other. Write the length of the hypotenuse as a function of the length of the shorter leg. c x 2x

  9. Guided Practice Write the specified quantity as a function of the specified variable. In some cases, it may be helpful to draw a picture. A square is inscribed in a circle. Write the area of the square as a function of the radius of the circle. 2r s s

  10. An isosceles triangle has its base along the x-axis with one base vertex at the origin and its vertex in the first quadrant on the graph of . Write the area of the triangle as a function of the length of the base.

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