Solve the Problem Book Sales Vs $y = a + b \ln t$

question 51

Multiple Choice

Solve the problem.
-The sales of a book tend to increase over the short-term as word-of-mouth makes the book "catch on." The number of books sold N(t) for a new novel t weeks after release at a certain book store is given In the table for the first 6 weeks.
$\begin{array}{c|c}\text { Weeks } t & \begin{array}{c}\text { Number } \\\text { Sold } N(t) \end{array} \\\hline 1 & 20 \\2 & 28 \\3 & 33 \\4 & 36 \\5 & 38 \\6 & 41\end{array}$

Book Sales vs. Weeks After Release



a. Find a model of the form $y = a + b \ln t$ .
b. Use the model to predict the sales in week 11. Round to the nearest whole unit.
c. Is it reasonable to assume that the logarithmic trend will continue? Why or why not?

• A) a. \(y = 3.9 + 19 \ln t\) b. 49 books c. Yes. The number of books sold will continue to increase although the sales will approach a limit.
• B) a. \(y = 20.1 + 11.5 \ln t\) b. 48 books c. Yes. The number of books sold will continue to increase although the sales will approach a limit.
• C) a. \(y = 3.9 + 19 \ln t\) b. 49 books c. No. The trend cannot continue indefinitely. At some point, book sales will begin to decrease as most reading enthusiasts have read the book.
• D) a. \(y = 20.1 + 11.5 \ln t\) b. 48 books c. No. The trend cannot continue indefinitely. At some point, book sales will begin to decrease as most reading enthusiasts have read the book.

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Definitions:

Altruism

The selfless concern for the well-being of others without expecting any reward.

Prosocial Behavior

Behaviors aimed at supporting other individuals, encompassing activities such as aiding, contributing, giving, collaborating, and offering voluntary assistance.

Prosocial Behavior

Actions intended to benefit others, including helping, sharing, donating, and volunteering.

Altruism

The selfless concern for the well-being of others, often leading to helping behaviors without expectation of personal gain.