A publishing company estimates that when a new book by a best-selling American author first hits the market, its sales can be predicted by the equation , where represents the total number (in thousands) of copies of the book sold in the United States by the end of the xth week. The number of copies of the book sold abroad by the end of the xth week can be modeled by thousand copies of the book How many books will be sold by the end of the first year (that is, 52 weeks)?
A) 497,278 books
B) 503,778 books
C) 6,500 books
D) 490,778 books
E) 4,907 books

Question

A publishing company estimates that when a new book by a best-selling American author first hits the market, its sales can be predicted by the equation  , where  represents the total number (in thousands) of copies of the book sold in the United States by the end of the xth week. The number of copies of the book sold abroad by the end of the xth week can be modeled by  thousand copies of the book How many books will be sold by the end of the first year (that is, 52 weeks)?
A) 497,278 books 
B) 503,778 books 
C) 6,500 books 
D) 490,778 books 
E) 4,907 books

Quizplus · Accepted Answer

To find the total number of books sold in one year (52 weeks), we need to add up the number of books sold each week from 1 to 52. We can do this using integration:

∫_0^52(11e^(0.125x))dx = [(88/125)e^(0.125x)]_0^52 = (88/125)(e^(6.5) - 1) ≈ 503,778

Therefore, the total number of books sold in one year is approximately 503,778. The closest answer choice is B.

A Publishing Company Estimates That When a New Book by a Best-Selling