Final answer:
To obtain the linear function representing the page length of the book as a function of the edition number, we can use the information given: the second edition was 583 pages long and the sixth edition was 749 pages long. The slope of the linear function is 41.5 pages per edition, meaning that the book is growing at a rate of 41.5 pages per edition. By the 25th edition, the book will have grown to over 1,500 pages.
Step-by-step explanation:
To obtain the linear function that represents the page length of the book as a function of the edition number, we can use the information given: the second edition was 583 pages long and the sixth edition was 749 pages long. We can use these two points to find the slope, which represents the rate at which the length of the book is growing per edition, and the y-intercept, which represents the length of the book at edition 0.
The slope can be found by using the formula: slope = (change in y)/(change in x). In this case, the change in y is 749 - 583 = 166, and the change in x is 6 - 2 = 4. So, the slope is 166/4 = 41.5 pages per edition.
The linear function representing the page length L as a function of the edition number n is therefore L(n) = 41.5n + b, where b is the y-intercept. To find the y-intercept, we can substitute the values of n and L from one of the given points into the equation. Let's use the second edition where n = 2 and L = 583: 583 = 41.5(2) + b. Solving for b gives us b = 583 - 83 = 500.
So, the linear function representing the page length of the book as a function of the edition number is L(n) = 41.5n + 500.
(b) The units of measurement of the slope are pages per edition. The slope tells us that for every one edition increase, the book grows by an average of 41.5 pages.
(c) To find the edition at which the book will have grown to over 1,500 pages, we can set the linear function equal to 1,500 and solve for n. 1,500 = 41.5n + 500. Subtracting 500 from both sides gives us 1,000 = 41.5n. Dividing both sides by 41.5 gives us n = 24.10. Since the edition number must be a whole number, rounding up to the nearest whole number gives us n = 25.