Section 1.10 Modeling with Functions

1
Section 1.10Modeling with Functions
2

• Construct Functions from Verbal Descriptions

3
Example
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.
4
Continued on the next slide
5
(No Transcript)
6
Example
7
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?
8
Graphing Calculator
Solving the previous problem using intersection.
Let y1 be the left side of the equation and y2 be
the right side of the equation.
9
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?
10
Continued on the next slide
11
Number of Passengers Per Month
Revenue Per Month
12
(No Transcript)
13

• Functions from Formulas

14
(No Transcript)
15
Example
A 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.
x
x
9
14
16
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
17
Modeling the Area of a Rectangle Given a Specific
Perimeter
18
Example
You 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
19
Annual Simple Interest on an investment
20
Example
A 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 years 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
21
(No Transcript)
22
Figure 1.80
Continued on the next slide
23
(No Transcript)
24
Example
If a cylindrical can is to hold 50 cubic inches
of oil. Write the surface area of the cylinder in
terms of r.
25
(No Transcript)
26
(No Transcript)
27
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
(x,y)
28
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.
(a) I5(2000x)3x (b) I.05(2000x).03x (c)
I.05(2000-x).03x (d) I5(2000-x)3x
29
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) (b) (c) (d)