example 5 Marijuana Use

Chapter 3.2

For the years 1991 through 2006, the percent p of high school seniors who have triedmarijuana can be considered as a function of the time t according to the model

where t is the number of years after 1990.

a. Find the year(s) after 1995 during which the percent is predicted to be 40, using a graphical method.

b. Verify the solution(s) numerically. (Source: National Institute on Drug Abuse)

20.1967 4.0630 27.7455p t t

2009 PBLPathways

2009 PBLPathways

For the years 1991 through 2006, the percent p of high school seniors who have triedmarijuana can be considered as a function of the time t according to the model

where t is the number of years after 1990.

a. Find the year(s) after 1995 during which the percent is predicted to be 40, using a graphical method.

b. Verify the solution(s) numerically. (Source: National Institute on Drug Abuse)

20.1967 4.0630 27.7455p t t

2009 PBLPathways

For the years 1991 through 2006, the percent p of high school seniors who have triedmarijuana can be considered as a function of the time t according to the model

where t is the number of years after 1990.

a. Find the year(s) after 1995 during which the percent is predicted to be 40, using a graphical method.

20.1967 4.0630 27.7455p t t

2009 PBLPathways

For the years 1991 through 2006, the percent p of high school seniors who have triedmarijuana can be considered as a function of the time t according to the model

where t is the number of years after 1990.

a. Find the year(s) after 1995 during which the percent is predicted to be 40, using a graphical method.

20.1967 4.0630 27.7455p t t

2 1

240 0.1967 4.0630 27.7455y y

t t

2009 PBLPathways

For the years 1991 through 2006, the percent p of high school seniors who have triedmarijuana can be considered as a function of the time t according to the model

where t is the number of years after 1990.

a. Find the year(s) after 1995 during which the percent is predicted to be 40, using a graphical method.

20.1967 4.0630 27.7455p t t

2 1

240 0.1967 4.0630 27.7455y y

t t

2009 PBLPathways

For the years 1991 through 2006, the percent p of high school seniors who have triedmarijuana can be considered as a function of the time t according to the model

where t is the number of years after 1990.

a. Find the year(s) after 1995 during which the percent is predicted to be 40, using a graphical method.

20.1967 4.0630 27.7455p t t

2 1

240 0.1967 4.0630 27.7455y y

t t

y2

y1

t

p

2009 PBLPathways

For the years 1991 through 2006, the percent p of high school seniors who have triedmarijuana can be considered as a function of the time t according to the model

where t is the number of years after 1990.

a. Find the year(s) after 1995 during which the percent is predicted to be 40, using a graphical method.

20.1967 4.0630 27.7455p t t

2 1

240 0.1967 4.0630 27.7455y y

t t

y2

y1

t

p

2009 PBLPathways

For the years 1991 through 2006, the percent p of high school seniors who have triedmarijuana can be considered as a function of the time t according to the model

where t is the number of years after 1990.

a. Find the year(s) after 1995 during which the percent is predicted to be 40, using a graphical method.

20.1967 4.0630 27.7455p t t

2 1

240 0.1967 4.0630 27.7455y y

t t

(3.67, 40) (16.99, 40)

y2

y1

t

p

2009 PBLPathways

For the years 1991 through 2006, the percent p of high school seniors who have triedmarijuana can be considered as a function of the time t according to the model

where t is the number of years after 1990.

a. Find the year(s) after 1995 during which the percent is predicted to be 40, using a graphical method.

20.1967 4.0630 27.7455p t t

2 1

240 0.1967 4.0630 27.7455y y

t t

(3.67, 40) (16.99, 40)

y2

y1

X

t

p

2009 PBLPathways

For the years 1991 through 2006, the percent p of high school seniors who have triedmarijuana can be considered as a function of the time t according to the model

where t is the number of years after 1990.

b. Verify the solution(s) numerically.

20.1967 4.0630 27.7455p t t

2009 PBLPathways

For the years 1991 through 2006, the percent p of high school seniors who have triedmarijuana can be considered as a function of the time t according to the model

where t is the number of years after 1990.

b. Verify the solution(s) numerically.

20.1967 4.0630 27.7455p t t

2 1

240 0.1967 4.0630 27.7455y y

t t

t y1 y2

2009 PBLPathways

For the years 1991 through 2006, the percent p of high school seniors who have triedmarijuana can be considered as a function of the time t according to the model

where t is the number of years after 1990.

b. Verify the solution(s) numerically.

20.1967 4.0630 27.7455p t t

2 1

240 0.1967 4.0630 27.7455y y

t t

t y1 y2

14

15

16

17

18

2009 PBLPathways

For the years 1991 through 2006, the percent p of high school seniors who have triedmarijuana can be considered as a function of the time t according to the model

where t is the number of years after 1990.

b. Verify the solution(s) numerically.

20.1967 4.0630 27.7455p t t

2 1

240 0.1967 4.0630 27.7455y y

t t

t y1 y2

14 46.074 40

15 44.433 40

16 42.398 40

17 39.97 40

18 37.149 40

2009 PBLPathways

For the years 1991 through 2006, the percent p of high school seniors who have triedmarijuana can be considered as a function of the time t according to the model

where t is the number of years after 1990.

b. Verify the solution(s) numerically.

20.1967 4.0630 27.7455p t t

2 1

240 0.1967 4.0630 27.7455y y

t t

t y1 y2

14 46.074 40

15 44.433 40

16 42.398 40

17 39.97 40

18 37.149 40