BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1, Problem 3P

a.

To determine

Make a scatter plot of the data.

Expert Solution

Answer to Problem 3P

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 3P , additional homework tip  1

Explanation of Solution

Given information:

To estimate ages of trees, forest rangers use a linear model that relates tree diameter to age. The model is useful because tree diameter is much easier to measure than tree age (which requires special tools for extracting a representative cross-section of the tree and counting the rings). To find the model, use the data in the table, which were collected for a certain variety of oaks.

Calculation:

The scatter plot of the data is given as,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 3P , additional homework tip  2

Hence, the graph is shown above.

b.

To determine

Find and graph a linear function that models the data.

Expert Solution

Answer to Problem 3P

  y=6.451x0.1523

Explanation of Solution

Given information:

To estimate ages of trees, forest rangers use a linear model that relates tree diameter to age. The model is useful because tree diameter is much easier to measure than tree age (which requires special tools for extracting a representative cross-section of the tree and counting the rings). To find the model, use the data in the table, which were collected for a certain variety of oaks.

Calculation:

Using a calculator, we find the following regression line that models the data in the form of,

  y=ax+b

Using regression calculator,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 3P , additional homework tip  3

Substituting a=6.451 and b=0.1523 , we get,

  y=6.451x0.1523

Hence, the linear function that models the data is y=6.451x0.1523 .

c.

To determine

Use the model to estimate the age of an oak whose diameter is 18in.

Expert Solution

Answer to Problem 3P

  116 years.

Explanation of Solution

Given information:

To estimate ages of trees, forest rangers use a linear model that relates tree diameter to age. The model is useful because tree diameter is much easier to measure than tree age (which requires special tools for extracting a representative cross-section of the tree and counting the rings). To find the model, use the data in the table, which were collected for a certain variety of oaks.

Calculation:

The diameter 18in. corresponds x=18 to in our model. The model gives,

  y=6.451(18)0.1523y=116

Hence, the estimated age of an oak whose diameter is 18in. is 116 years.

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