Chapter 4.1, Problem 24PPS

a.

To determine

To calculate: An equation in slope intercept form to find the cost C of a dictionary y years after 1904.

Answer to Problem 24PPS

The cost C of a dictionary y years after 1904 will be $C=30+6y$

Explanation of Solution

Given:

In 1904, a dictionary cost 30¢. Since then the cost of a dictionary has risen an average of 6¢ per year.

Calculation:

The cost of a dictionary in 1904 $=$ 30¢

Increase in cost in 1 year after 1904 $=$ 6¢

Then, increase in cost iny years after 1904 $=6y$ ¢

Then, y years after 1904 the total cost of a dictionary

  $=$ (The cost of a dictionary in 1904 + increase in cost in y years)

  $=30+6y$

Here, C represents the cost of a dictionary.

Then, $C=30+6y$

Conclusion:

The cost C of a dictionary y years after 1904 will be $C=30+6y$

b.

To determine

To calculate:The cost of a dictionary in 2025.

Answer to Problem 24PPS

The cost of a dictionary in 2025 will be 756¢.

Explanation of Solution

Given:

In 1904, a dictionary cost 30¢. Since then the cost of a dictionary has risen an average of 6¢ per year.

Calculation:

Number of years between 2025 and 1904 $=2025-1904=121$ years

The cost C of a dictionary y years after 1904 is given by, $C=30+6y$

Then cost of a dictionary 121 years after 1904

  $\begin{array}{l}=30+6\times 121\\ =30+726\\ =756\end{array}$

Conclusion:

The cost of a dictionary in 2025 will be 756¢.