The number of visitors P to a website in a given week over a 1-year period is given by P(t)=125+(t−80)e^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.
The number of visitors P to a website in a given week over a 1-year period is given by P(t)=125+(t−80)e^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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Question
The number of visitors P to a website in a given week over a 1-year period is given by P(t)=125+(t−80)e^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.
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) = 125 + (t- 80) e 0.021 where tis the week and 1sts 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.
a) The number of visitors is decreasing over the interval (1,30).
(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 (30,52).
(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 (30,33.894)
(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 maximized in week 30 at approximately 34 visitors.
(Round to the nearest integer as needed.)
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