khynia11
15.04.2020 •
Mathematics
The publisher of a recently released nonfiction book expects that over the first 20 months after its release, the monthly profit can be approximated with the model P(t) 240t - 40t t2 +20 where P is in thousands of dollars and t is in months from the time of release. a. Derive a model that gives the marginal profit of the book. P'(t) Preview b. Specify the expected marginal profit 5 months after release. Round to 2 decimal places thousands of dollars per month c. Specify the expected marginal profit 11 months after release. Round to 2 decimal places. thousands of dollars per month d. After which month is the monthly profit start to decrease steadily?
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Ответ:
(a)
(b)P'(5)=-($4.54) Thousand
(c)P'(11)=-($2.10) Thousand
(d)The fifth Month
Step-by-step explanation:
Given the monthly profit model:
(a)We want to derive a model that gives the Marginal Profit, P' of the book.
We differentiate
using quotient rule.
Simplifying
We have derived a model for the marginal profit.
(b) After 5 months, at t=5
Marginal Profit=P'(5)
=-($4.54) Thousand of dollars
(c)Marginal Profit 11 Months after book release
=-($2.10) Thousand of dollars
(d) Since the marginal profit at t=5 is negative, after the 5th Month, the profit starts to experience a steady decrease.
Ответ:
c...
Step-by-step explanation: