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