section 1.10 modeling with functions
DESCRIPTION
Section 1.10 Modeling with Functions. Construct Functions from Verbal Descriptions. Example. Write the function that will solve this problem. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/1.jpg)
Section 1.10Modeling with Functions
![Page 2: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/2.jpg)
Construct Functions from Verbal Descriptions
![Page 3: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/3.jpg)
Write the function that will solve this problem.
Spice Drops candy calorie count exceeds Smarties candy calorie count by 70 calories per serving. If the sum of one serving of each candy equals 190 calories find the calorie count of each kind of candy.
Example
![Page 4: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/4.jpg)
Continued on the next slide
![Page 5: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/5.jpg)
![Page 6: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/6.jpg)
Example
![Page 7: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/7.jpg)
Example Write the functions for men and women and solve the problem.The percentage of women in the labor force and the percentage of men in the labor force is illustrated in the graph at left. The decrease yearly of men in the labor force is ¼% and the increase in women in the labor force is ½%. If there are presently 70 million men and 60 million women in the labor force, when will the number of both sexes be equal?
![Page 8: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/8.jpg)
Graphing CalculatorSolving the previous problem using intersection. Let y1 be the left side of the equation and y2 be the right side of the equation.
1=70-.0025 70 xy 2 60 .005 60 xy
![Page 9: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/9.jpg)
Example
A local telephone company charges $11 for local phone service and an additional $ .10 for each long distance phone call. A second local telephone company charges $14 for local service and an additional $ .05 for each long distance phone call. For how many minutes of long-distance calls will the costs for the two companies be the same?
![Page 10: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/10.jpg)
Continued on the next slide
![Page 11: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/11.jpg)
Number of Passengers Per Month
Revenue Per Month
![Page 12: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/12.jpg)
2
2
Any function in the form f(x)=ax where a 0, is called a quadratic function. In this chapter we use the U-shaped graph
of the stadard quadratic function, f(x)=xto graph various transformations.
bx c
![Page 13: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/13.jpg)
Functions from Formulas
![Page 14: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/14.jpg)
![Page 15: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/15.jpg)
ExampleA machine produces open boxes using rectangular sheets of metal measuring 14 inches by 9 inches. The machine cuts equal-sized squares from each corner. Then it shapes the metal into an open box by turning up the sides. Express the volume of the box, V, in cubic inches as a function of the length of the side of the square cut from each corner, x, in inches.
9”
14”
xx
![Page 16: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/16.jpg)
Modeling the Area of a Rectangle Given a Specific Perimeter
Possible Lengths and Widths if the Perimeter is 140 feet
Continued oon the next slide
![Page 17: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/17.jpg)
Modeling the Area of a Rectangle Given a Specific Perimeter
![Page 18: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/18.jpg)
ExampleYou have 300 feet of fencing to fence in a corral for your horse. Express the area of the fenced in area as a function of one of its dimensions.
? - x
![Page 19: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/19.jpg)
Annual Simple Interest on an investment
The annual simple interest that an investment earns is given by the formulaI=Prwhere I is the simple interest, P is the principal, and r is the simple interest rate expressed in decimal form. Suppose that you deposit $400 at 3% (r=0.03). I=$400 x .03=$12
![Page 20: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/20.jpg)
ExampleA woman who was going to retire had $100,000 that she invested in her local bank. She put some of the money in a money market account at 3 ½% and some in a certificate of deposit at 4%. If the first year’s interest is $3850, how much money did she put in each account?
Write the functions you would use to solve this problem.
% amount Interest
Money market
CD
![Page 21: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/21.jpg)
![Page 22: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/22.jpg)
Continued on the next slide
Figure 1.80
![Page 23: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/23.jpg)
![Page 24: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/24.jpg)
ExampleIf a cylindrical can is to hold 50 cubic inches of oil. Write the surface area of the cylinder in terms of “r.”
![Page 25: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/25.jpg)
![Page 26: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/26.jpg)
![Page 27: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/27.jpg)
Example
Find the distance from the point on the parabola to the origin. Express it as a function of x. The parabola can be described as
2 3y x
x
y
(x,y)
![Page 28: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/28.jpg)
(a) I=5(2000+x)+3x
(b) I=.05(2000+x)+.03x
(c) I=.05(2000-x)+.03x
(d) I=5(2000-x)+3x
If you invest a total of $2000 in two accounts. One account pays 5% and another account pays 3%. Write the equation that expresses the amount of interest that you will make in 1 year in terms of x, the amount invested at 3%.
![Page 29: Section 1.10 Modeling with Functions](https://reader036.vdocument.in/reader036/viewer/2022062816/56813a7e550346895da27a27/html5/thumbnails/29.jpg)
(a)
(b)
(c)
(d)
You have 400 meters of fencing to fence in a garden. Write the formula for the area of the garden as a function of x its width.
A=x(70-x)A=x(400-x)A=x(400+x)A=x(200-x)