The second edition of a textbook was 575 pages long. By the time it got to the seventh edition, the book had grown to 757 pages.(a)Use this information to obtain the page length L as a linear function of the edition number n.L(n) = (b)What are the units of measurement of the slope?editions per pagepages per edition What does the slope tell you about the length of the book?The book is growing at a rate of pages per edition.(c)At this rate, by which edition will the book have grown to over 1,500 pages? (Round your answer up to the nearest whole number.)The book will have grown to over 1,500 pages by edition number .
Question
The second edition of a textbook was 575 pages long. By the time it got to the seventh edition, the book had grown to 757 pages.(a)Use this information to obtain the page length L as a linear function of the edition number n.L(n) = (b)What are the units of measurement of the slope?editions per pagepages per edition What does the slope tell you about the length of the book?The book is growing at a rate of pages per edition.(c)At this rate, by which edition will the book have grown to over 1,500 pages? (Round your answer up to the nearest whole number.)The book will have grown to over 1,500 pages by edition number .
Solution
(a) To obtain the page length L as a linear function of the edition number n, we first need to find the slope of the line. The slope is the change in page length divided by the change in edition number.
The change in page length is 757 - 575 = 182 pages. The change in edition number is 7 - 2 = 5 editions.
So, the slope is 182/5 = 36.4 pages per edition.
The second edition of the book was 575 pages long, so the y-intercept (b) is 575 - 2*36.4 = 502.2 pages.
Therefore, the linear function is L(n) = 36.4n + 502.2.
(b) The units of measurement of the slope are pages per edition. This means that for each new edition, the book grows by 36.4 pages.
(c) To find out by which edition the book will have grown to over 1,500 pages, we can set L(n) = 1500 and solve for n.
1500 = 36.4n + 502.2 997.8 = 36.4n n = 997.8 / 36.4 = 27.4
Since we can't have a fraction of an edition, we round up to the nearest whole number. Therefore, the book will have grown to over 1,500 pages by edition number 28.
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