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) = 13t t² +90 +0.19 (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 month the recognition will increase about IP(6)| percent. O In the next month the recognition will decrease about IP'(6)| percent. O In the next IP(6)| months the recognition will decrease about 1%. O In the next IP'(6)| months the recognition will increase about 1%. (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 decrease about IP'(12)| percent. O In the next month the recognition will increase about IP (12)| percent. O In the next IP'(12)| months the recognition will decrease about 1%. O In the next | P'(12)| months the recognition will increase about 1%. (c) One month prior to the election, is it better for P'(t) to be positive or negative? Explain. O Negative is better because it means decreasing recognition. O Negative is better because it means increasing recognition. O Positive is better because it means decreasing recognition. O Positive 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) = 13t t² +90 +0.19 (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 month the recognition will increase about IP(6)| percent. O In the next month the recognition will decrease about IP'(6)| percent. O In the next IP(6)| months the recognition will decrease about 1%. O In the next IP'(6)| months the recognition will increase about 1%. (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 decrease about IP'(12)| percent. O In the next month the recognition will increase about IP (12)| percent. O In the next IP'(12)| months the recognition will decrease about 1%. O In the next | P'(12)| months the recognition will increase about 1%. (c) One month prior to the election, is it better for P'(t) to be positive or negative? Explain. O Negative is better because it means decreasing recognition. O Negative is better because it means increasing recognition. O Positive is better because it means decreasing recognition. O Positive is better because it means increasing recognition.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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) =
13t
² +90
+ 0.19
(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 month the recognition will increase about IP'(6)| percent.
O In the next month the recognition will decrease about IP'(6)| percent.
O In the next IP'(6)| months the recognition will decrease about 1%.
O In the next IP(6)| months the recognition will increase about 1%.
(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 decrease about |P (12)| percent.
O In the next month the recognition will increase about IP'(12)| percent.
O In the next |P'(12)| months the recognition will decrease about 1%.
O In the next IP'(12)| months the recognition will increase about 1%.
(c) One month prior to the election, is it better for P'(t) to be positive or negative? Explain.
O Negative is better because it means decreasing recognition.
O Negative is better because it means increasing recognition.
O Positive is better because it means decreasing recognition.
O Positive is better because it means increasing recognition.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
