example 1
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example 1 Life Span
Chapter 5.7
The data in Table 5.25 show the expected life span of people for certain birth yearsin the United States. A technology-determined logistic function for the life-spandata is
where x is the number of birth years after 1900. The graph of this logistic function isshown below. Use this model to
0.0255
81.837 years
1 0.8213 xy
e
a. Estimate the expected life span of a person born in the United States in 1955 and a person born in 1980.
b. Find an upper limit for a person’s expected life span according to this model.
y
x
2009 PBLPathways
2009 PBLPathways
The data in Table 5.25 show the expected life span of people for certain birth yearsin the United States. A technology-determined logistic function for the life-spandata is
where x is the number of birth years after 1900. The graph of this logistic function isshown below. Use this model to
a. Estimate the expected life span of a person born in the United States in 1955 and a person born in 1980.
b. Find an upper limit for a person’s expected life span according to this model.
y
x
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
0.0255
81.837 years
1 0.8213 xy
e
a. Estimate the expected life span of a person born in the United States in 1955 and a person born in 1980.
Expected life span of person born in 1955
Expected life span of person born in 1980
55x 0.255 55
81.837
1 0.821368.1
ye
80x 0.255 80
81.837
1 0.821373.9
ye
2009 PBLPathways
a. Estimate the expected life span of a person born in the United States in 1955 and a person born in 1980.
Expected life span of person born in 1955
Expected life span of person born in 1980
55x 0.255 55
81.837
1 0.821368.1
ye
80x 0.255 80
81.837
1 0.821373.9
ye
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
a. Estimate the expected life span of a person born in the United States in 1955 and a person born in 1980.
Expected life span of person born in 1955
Expected life span of person born in 1980
55x 0.255 55
81.837
1 0.8213
68.1
ye
80x 0.255 80
81.837
1 0.821373.9
ye
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
a. Estimate the expected life span of a person born in the United States in 1955 and a person born in 1980.
Expected life span of person born in 1955
Expected life span of person born in 1980
55x 0.0255 55
81.837
1 0.8213
68.1
ye
80x 0.255 80
81.837
1 0.821373.9
ye
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
a. Estimate the expected life span of a person born in the United States in 1955 and a person born in 1980.
Expected life span of person born in 1955
Expected life span of person born in 1980
55x 0.0255 55
81.837
1 0.8213
68.1
ye
80x 0.255 80
81.837
1 0.821373.9
ye
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
a. Estimate the expected life span of a person born in the United States in 1955 and a person born in 1980.
Expected life span of person born in 1955
Expected life span of person born in 1980
55x 0.0255 55
81.837
1 0.8213
68.1
ye
80x 0.255 80
81.837
1 0.8213
73.9
ye
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
a. Estimate the expected life span of a person born in the United States in 1955 and a person born in 1980.
Expected life span of person born in 1955
Expected life span of person born in 1980
55x 0.0255 55
81.837
1 0.8213
68.1
ye
80x 0.255 80
81.837
1 0.8213
73.9
ye
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
a. Estimate the expected life span of a person born in the United States in 1955 and a person born in 1980.
Expected life span of person born in 1955
Expected life span of person born in 1980
55x 0.0255 55
81.837
1 0.8213
68.1
ye
80x 0.0255 80
81.837
1 0.8213
73.9
ye
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
a. Estimate the expected life span of a person born in the United States in 1955 and a person born in 1980.
Expected life span of person born in 1955
Expected life span of person born in 1980
55x 0.0255 55
81.837
1 0.8213
68.1
ye
80x 0.0255 80
81.837
1 0.8213
73.9
ye
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
b. Find an upper limit for a person’s expected life span according to this model.
x y
100 76.905
150 80.396
200 81.429
250 81.723
300 81.805
350 81.828
400 81.835
x
y
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
b. Find an upper limit for a person’s expected life span according to this model.
x y
100 76.905
150 80.396
200 81.429
250 81.723
300 81.805
350 81.828
400 81.835
x
y
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
b. Find an upper limit for a person’s expected life span according to this model.
x y
100 76.905
150 80.396
200 81.429
250 81.723
300 81.805
350 81.828
400 81.835
x
y
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
b. Find an upper limit for a person’s expected life span according to this model.
x y
100 76.905
150 80.396
200 81.429
250 81.723
300 81.805
350 81.828
400 81.835
x
y
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
b. Find an upper limit for a person’s expected life span according to this model.
x y
100 76.905
150 80.396
200 81.429
250 81.723
300 81.805
350 81.828
400 81.835
x
y
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
b. Find an upper limit for a person’s expected life span according to this model.
x y
100 76.905
150 80.396
200 81.429
250 81.723
300 81.805
350 81.828
400 81.835
x
y
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
b. Find an upper limit for a person’s expected life span according to this model.
x y
100 76.905
150 80.396
200 81.429
250 81.723
300 81.805
350 81.828
400 81.835
x
y
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
b. Find an upper limit for a person’s expected life span according to this model.
x y
100 76.905
150 80.396
200 81.429
250 81.723
300 81.805
350 81.828
400 81.835
x
y
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
b. Find an upper limit for a person’s expected life span according to this model.
x y
100 76.905
150 80.396
200 81.429
250 81.723
300 81.805
350 81.828
400 81.835
x
y
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
b. Find an upper limit for a person’s expected life span according to this model.
x y
100 76.905
150 80.396
200 81.429
250 81.723
300 81.805
350 81.828
400 81.835
x
y
0.0255
81.837 years
1 0.8213 xy
e
2009 PBLPathways
b. Find an upper limit for a person’s expected life span according to this model.
x y
100 76.905
150 80.396
200 81.429
250 81.723
300 81.805
350 81.828
400 81.835
x
y81.837y
0.0255
81.837 years
1 0.8213 xy
e
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