Suppose that the proportion P of voters who recognize a candidate's name t months after the start of the campaign is given by the following equation. P(t) = 16t ²+110 + 0.11 (a) Find the rate of change of P when t = 6. (Round your answer to three decimal places.) P'(6) = ▸ Explain its meaning. O In the next | P'(6)| months the recognition will increase about 1%. O In the next |P'(6)| months the recognition will decrease about 1%. O In the next month the recognition will increase about IP'(6)] percent. In the next month the recognition will decrease about IP'(6)| percent. (b) Find the rate of change of P when t = 12. (Round your answer to three decimal places.) P'(12) = Explain its meaning. O In the next month the recognition will increase about |P'(12)| percent. O In the next month the recognition will decrease about IP'(12)| percent. O In the next IP'(12)| months the recognition will increase about 1%. O In the next IP'(12)| months the recognition will decrease about 1%. (c) One month prior to the election, is it better for P'(t) to be positive or negative? Explain, O Positive is better because it means increasing recognition. O Negative is better because it means decreasing recognition. O Positive is better because it means decreasing recognition. O Negative is better because it means increasing recognition.
Suppose that the proportion P of voters who recognize a candidate's name t months after the start of the campaign is given by the following equation. P(t) = 16t ²+110 + 0.11 (a) Find the rate of change of P when t = 6. (Round your answer to three decimal places.) P'(6) = ▸ Explain its meaning. O In the next | P'(6)| months the recognition will increase about 1%. O In the next |P'(6)| months the recognition will decrease about 1%. O In the next month the recognition will increase about IP'(6)] percent. In the next month the recognition will decrease about IP'(6)| percent. (b) Find the rate of change of P when t = 12. (Round your answer to three decimal places.) P'(12) = Explain its meaning. O In the next month the recognition will increase about |P'(12)| percent. O In the next month the recognition will decrease about IP'(12)| percent. O In the next IP'(12)| months the recognition will increase about 1%. O In the next IP'(12)| months the recognition will decrease about 1%. (c) One month prior to the election, is it better for P'(t) to be positive or negative? Explain, O Positive is better because it means increasing recognition. O Negative is better because it means decreasing recognition. O Positive is better because it means decreasing recognition. O Negative is better because it means increasing recognition.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Suppose that the proportion P of voters who recognize a candidate's name t months after the start of the campaign is given by the following equation.
P(t) =
16t
²+110
+ 0.11
(a) Find the rate of change of P when t = 6. (Round your answer to three decimal places.)
P'(6) =
Explain its meaning.
O In the next IP'(6)| months the recognition will increase about 1%.
O In the next IP (6)| months the recognition will decrease about 1%.
O In the next month the recognition will increase about IP'(6)| percent.
O In the next month the recognition will decrease about IP'(6)| percent.
(b) Find the rate of change of P when t = 12. (Round your answer to three decimal places.)
P'(12) =
Explain its meaning.
O In the next month the recognition will increase about IP'(12)| percent.
O In the next month the recognition will decrease about IP'(12)| percent.
O In the next IP'(12)| months the recognition will increase about 1%.
O In the next IP'(12)| months the recognition will decrease about 1%.
(c) One month prior to the election, is it better for P'(t) to be positive or negative? Explain.
O Positive is better because it means increasing recognition.
O Negative is better because it means decreasing recognition.
O Positive is better because it means decreasing recognition.
O Negative is better because it means increasing recognition.
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