example 5 Inmate Population

Chapter 1.4

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

a. What is the rate of growth of people incarcerated from 1990 to 2000?

b. Write the linear equation that models the number N of prisoners as a function of the year x.

c. The Bureau of Justice Statistics projected that 2.29 million people will be incarcerated in 2005. Does your model agree with this projection? (Source: Bureau of Justice Statistics)

2009 PBLPathways

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

a. What is the rate of growth of people incarcerated from 1990 to 2000?

Two points: (1990, 1.15) and (2000, 1.91)

1.91 1.15 million peopleslope

2000 1990 year

0.76

100.076

million people per year

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

a. What is the rate of growth of people incarcerated from 1990 to 2000?

Two points: (1990, 1.15) and (2000, 1.91)

1.91 1.15 million peopleslope

2000 1990 year

0.76

100.076

million people per year

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

a. What is the rate of growth of people incarcerated from 1990 to 2000?

Two points: (1990, 1.15) and (2000, 1.91)

1.91 1.15 million peopleslope

2000 1990 year

0.76

100.076

million people per year

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

a. What is the rate of growth of people incarcerated from 1990 to 2000?

Two points: (1990, 1.15) and (2000, 1.91)

1.91 1.15 million peopleslope

2000 1990 year

0.76

100.076

million people per year

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

a. What is the rate of growth of people incarcerated from 1990 to 2000?

Two points: (1990, 1.15) and (2000, 1.91)

1.91 1.15 million peopleslope

2000 1990 year

0.76

100.076

million people per year

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

a. What is the rate of growth of people incarcerated from 1990 to 2000?

Two points: (1990, 1.15) and (2000, 1.91)

1.91 1.15 million peopleslope

2000 1990 year

0.76

100.076

million people per year

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

a. What is the rate of growth of people incarcerated from 1990 to 2000?

Two points: (1990, 1.15) and (2000, 1.91)

1.91 1.15 million peopleslope

2000 1990 year

0.76

100.076

million people per year

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

a. What is the rate of growth of people incarcerated from 1990 to 2000?

Two points: (1990, 1.15) and (2000, 1.91)

1.91 1.15 million peopleslope

2000 1990 year

0.76

100.076

million people per year

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

b. Write the linear equation that models the number N of prisoners as a function of the year x.

1 1

1 1

1.91 0.076 2000

1.91 0.076 152

0.076 150.09

y y m x x

N N m x x

N x

N x

N x

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

b. Write the linear equation that models the number N of prisoners as a function of the year x.

1 1

1 1

1.91 0.076 2000

1.91 0.076 152

0.076 150.09

y y m x x

N N m x x

N x

N x

N x

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

b. Write the linear equation that models the number N of prisoners as a function of the year x.

1 1

1 1

1.91 0.076 2000

1.91 0.076 152

0.076 150.09

y y m x x

N N m x x

N x

N x

N x

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

b. Write the linear equation that models the number N of prisoners as a function of the year x.

1 1

1 1

1.91 0.076 2000

1.91 0.076 152

0.076 150.09

y y m x x

N N m x x

N x

N x

N x

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

b. Write the linear equation that models the number N of prisoners as a function of the year x.

1 1

1 1

1.91 0.076 2000

1.91 0.076 152

0.076 150.09

y y m x x

N N m x x

N x

N x

N x

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

b. Write the linear equation that models the number N of prisoners as a function of the year x.

1 1

1 1

1.91 0.076 2000

1.91 0.076 152

0.076 150.09

y y m x x

N N m x x

N x

N x

N x

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

b. Write the linear equation that models the number N of prisoners as a function of the year x.

1 1

1 1

1.91 0.076 2000

1.91 0.076 152

0.076 150.09

y y m x x

N N m x x

N x

N x

N x

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

b. Write the linear equation that models the number N of prisoners as a function of the year x.

1 1

1 1

1.91 0.076 2000

1.91 0.076 152

0.076 150.09

y y m x x

N N m x x

N x

N x

N x

( ) 0.076 150.09N x x

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

c. The Bureau of Justice Statistics projected that 2.29 million people will be incarcerated in 2005. Does your model agree with this projection? (Source: Bureau of Justice Statistics)

(2005) 0.076 2005 150.09

152.38 150.09

2.29

N

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

c. The Bureau of Justice Statistics projected that 2.29 million people will be incarcerated in 2005. Does your model agree with this projection? (Source: Bureau of Justice Statistics)

(2005) 0.076 2005 150.09

152.38 150.09

2.29

N

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

c. The Bureau of Justice Statistics projected that 2.29 million people will be incarcerated in 2005. Does your model agree with this projection? (Source: Bureau of Justice Statistics)

(2005) 0.076 2005 150.09

152.38 150.09

2.29

N

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

c. The Bureau of Justice Statistics projected that 2.29 million people will be incarcerated in 2005. Does your model agree with this projection? (Source: Bureau of Justice Statistics)

(2005) 0.076 2005 150.09

152.38 150.09

2.29

N

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

c. The Bureau of Justice Statistics projected that 2.29 million people will be incarcerated in 2005. Does your model agree with this projection? (Source: Bureau of Justice Statistics)

(2005) 0.076 2005 150.09

152.38 150.09

2.29

N

2009 PBLPathways

The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15 million people being incarcerated in 1990 and 1.91 million incarcerated in 2000.

c. The Bureau of Justice Statistics projected that 2.29 million people will be incarcerated in 2005. Does your model agree with this projection? (Source: Bureau of Justice Statistics)

(2005) 0.076 2005 150.09

152.38 150.09

2.29

N

million people