Assignment:
Part I
Q1. Cell Phones The following table gives the number of millions of U.S. cellular telephone subscribers.
a. Create a scatter plot for the data with x equal to the number of years from 1985. Does it appear that the data could be modeled with a quadratic function?
b. Find the quadratic function that is the best fit for these data, with x equal to the number of years from 1985 and y equal to the number of subscribers in millions?
c. Use the model to estimate the number in 2005.
d. What part of the U.S. population does this estimate equal?
|
Year
|
Subscribers(millions)
|
Year
|
Subscribers(millions)
|
|
1985
|
0.340
|
1994
|
24.134
|
|
1986
|
0.682
|
1995
|
33.786
|
|
1987
|
1.231
|
1996
|
44.043
|
|
1988
|
2.069
|
1997
|
55.312
|
|
1989
|
3.509
|
1998
|
69.209
|
|
1990
|
5.283
|
1999
|
86.047
|
|
1991
|
7.557
|
2000
|
107.478
|
|
1992
|
11.033
|
2001
|
128.375
|
|
1993
|
16.009
|
2002
|
140.767
|
Q2. World Population One projection of the world population by the United Nation for selected years (a low projection scenario) is given in the table below.
|
Year
|
Projected Population(million)
|
Year
|
Projected Population(million)
|
|
1995
|
5666
|
2075
|
6402
|
|
2000
|
6028
|
2100
|
5153
|
|
2025
|
7275
|
2125
|
4074
|
|
2050
|
7343
|
2150
|
3236
|
a. Find a quadratic function that fits these data, using the number of the years after 1990 as the input.
b. Find the positive x-intercept of this graph, to the nearest year.
c. When can we be certain that this model no longer applies?
Q3. Classroom Size The date in the table below give the number of students per teacher for selected years between 1960 and 1998.
|
Year
|
Students per Teacher
|
Year
|
Students per Teacher
|
|
1960
|
25.8
|
1992
|
17.4
|
|
1965
|
24.7
|
1993
|
17.4
|
|
1970
|
22.3
|
1994
|
17.3
|
|
1975
|
20.4
|
1995
|
17.3
|
|
1980
|
18.7
|
1996
|
17.1
|
|
1985
|
17.9
|
1997
|
17.0
|
|
1990
|
17.2
|
1998
|
17.2
|
|
1995
|
17.3
|
|
|
a. Find the power function that is the best fit for the data, using as input the number of years after 1950.
b. According to the unrounded model, how many students per teacher were there in 2000?
c. Is this function increasing or decreasing during this time period?
d. What does the model predict will happen to the number of student per teacher as time goes on?
Q4. Insurance Rates The following table gives the monthly insurance rates for a $100,000 life insurance policy for smokers 35-50 years of age.
a. Create a scatter plot for the data.
b. Does it appear that a quadratic function can be used to model the data? If so, find the best- fitting quadratic model?
c. Find the power model that is the best fit for the data.
d. Compare the two models by graphing each model on the same axes with the data points.
Which model appears to be better fit?
|
Age(yr)
|
Monthly Insurance Rate ($)
|
Age(yr)
|
Monthly Insurance Rate ($)
|
|
35
|
17.32
|
43
|
23.71
|
|
36
|
17.67
|
44
|
25.11
|
|
37
|
18.02
|
45
|
26.60
|
|
38
|
18.46
|
46
|
28.00
|
|
39
|
19.07
|
47
|
29.40
|
|
40
|
19.95
|
48
|
30.80
|
|
41
|
21.00
|
49
|
32.55
|
|
42
|
22.22
|
50
|
34.47
|
Part II
Q1. Population of Children The following table gives the estimate population (in millions) of U.S. boys age 5 and under and the estimate U.S. population (in millions) of girls age 5 and under in selected years.
|
Year
|
1995
|
2000
|
2005
|
2010
|
|
Boys
|
10.02
|
9.71
|
9.79
|
10.24
|
|
Girls
|
9.57
|
9.27
|
9.43
|
9.77
|
A function that models the population (in millions) of U.S. boys age 5 and under t years after 1990 is B(t) =0.0076t²-0.1752t+10.705, and a function that model the population (in millions) of U.S. girls age 5 and under t years after 1990 is G(t) =0.0064t² - 0.1448t+10.12.
a. Find the equation of a function that models the estimate U.S population (in millions) of children age 5 and under t years after 1990.
b. Use the result of part (a) to estimate the U.S population of children age 5 and under in 2003.
Part III
Q1. Education If the function f(x) gives the number of female PhDs produced by American universities x years after 1990 and the function g(x) gives the number of male PhDs produced by American universities x years after 1990, what function gives the total number of PhDs produced by American universities x years after 1990?
Q2. Projectiles Two projectiles are fired into the air over a lake, with the height of the first projectile given by y=100+130t-16t² and the height of the second projectile given by
y=-16t²+180t, where y is in feet and t is in seconds. Over what time interval, before the lower one hits the lake, is the second projectile above the first?
Provide complete and step by step solution for the question and show calculations and use formulas.