The number of visitors P to a website in a given week over a 1-year period is given by P(t) = 119 + (t-90)0.02t, where t is the week and 1≤t≤52. a) Over what interval of time during the 1-year period is the number of visitors decreasing? b) Over what interval of time during the 1-year period is the number of visitors increasing? c) Find the critical point, and interpret its meaning. www a) The number of visitors is decreasing over the interval (Simplify your answer. Type integers or decimals rounded to three decimal places as needed. Type your answer in interval notation.) b) The number of visitors is increasing over the interval (Simplify your answer. Type integers or decimals rounded to three decimal places as needed. Type your answer in interval notation.) c) The critical point is (Type an ordered pair. Type integers or decimals rounded to three decimal places as needed.) Interpret what the critical point means. The critical point means that the number of visitors was (Round to the nearest integer as needed.) ▼ in week at approximately visitors.
The number of visitors P to a website in a given week over a 1-year period is given by P(t) = 119 + (t-90)0.02t, where t is the week and 1≤t≤52. a) Over what interval of time during the 1-year period is the number of visitors decreasing? b) Over what interval of time during the 1-year period is the number of visitors increasing? c) Find the critical point, and interpret its meaning. www a) The number of visitors is decreasing over the interval (Simplify your answer. Type integers or decimals rounded to three decimal places as needed. Type your answer in interval notation.) b) The number of visitors is increasing over the interval (Simplify your answer. Type integers or decimals rounded to three decimal places as needed. Type your answer in interval notation.) c) The critical point is (Type an ordered pair. Type integers or decimals rounded to three decimal places as needed.) Interpret what the critical point means. The critical point means that the number of visitors was (Round to the nearest integer as needed.) ▼ in week at approximately visitors.
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
![The number of visitors \( P \) to a website in a given week over a 1-year period is given by:
\[ P(t) = 119 + (t - 90)e^{0.021} \]
where \( t \) is the week and \( 1 \leq t \leq 52 \).
**Questions:**
a) Over what interval of time during the 1-year period is the number of visitors decreasing?
b) Over what interval of time during the 1-year period is the number of visitors increasing?
c) Find the critical point, and interpret its meaning.
**Answers:**
a) The number of visitors is decreasing over the interval [ ].
(Simplify your answer. Type integers or decimals rounded to three decimal places as needed. Type your answer in interval notation.)
b) The number of visitors is increasing over the interval [ ].
(Simplify your answer. Type integers or decimals rounded to three decimal places as needed. Type your answer in interval notation.)
c) The critical point is ( ).
(Type an ordered pair. Type integers or decimals rounded to three decimal places as needed.)
Interpret what the critical point means.
The critical point means that the number of visitors was ▼ in week [ ] at approximately [ ] visitors.
(Round to the nearest integer as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ceb2d65-29b4-49d4-9830-4ba06589987b%2F6694b7c7-2808-4eaa-b430-2d985522b83e%2Fa2jr6rq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The number of visitors \( P \) to a website in a given week over a 1-year period is given by:
\[ P(t) = 119 + (t - 90)e^{0.021} \]
where \( t \) is the week and \( 1 \leq t \leq 52 \).
**Questions:**
a) Over what interval of time during the 1-year period is the number of visitors decreasing?
b) Over what interval of time during the 1-year period is the number of visitors increasing?
c) Find the critical point, and interpret its meaning.
**Answers:**
a) The number of visitors is decreasing over the interval [ ].
(Simplify your answer. Type integers or decimals rounded to three decimal places as needed. Type your answer in interval notation.)
b) The number of visitors is increasing over the interval [ ].
(Simplify your answer. Type integers or decimals rounded to three decimal places as needed. Type your answer in interval notation.)
c) The critical point is ( ).
(Type an ordered pair. Type integers or decimals rounded to three decimal places as needed.)
Interpret what the critical point means.
The critical point means that the number of visitors was ▼ in week [ ] at approximately [ ] visitors.
(Round to the nearest integer as needed.)
Expert Solution
Step 1: Introduction to given details
Step by step
Solved in 3 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,
