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?

(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.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.