John O'Hagan is considering upgrading the Web server equipment at OHaganBooks.com because of frequent crashes. The tech services manager has been monitoring the frequency of crashes as a function of website traffic (measured in thousands of visits per day) and has obtained the following model c(x) = (0.06x + 2 0.08x + 1 if 0 ≤ x ≤ 50 if x > 50, where c(x) is the average number of crashes in a day in which there are x thousand visitors. (a) On average, how many times will the website crash on a day when there are 10,000 visits? times On average, how many times will the website crash on a day when there are 50,000 visits? times On average, how many times will the website crash on a day when there are 100,000 visits? times (b) What does the coefficient 0.06 tell you about the website's stability? The coefficient 0.06 is the slope of the first formula, indicating that, for Web site traffic of up to 50 visits per day (0 ≤ x ≤ 50), the number of crashes is increasing by 0.06 per additional visit. O The coefficient 0.06 is the slope of the first formula, indicating that, for Web site traffic of up to 50,000 visits per day (0 ≤ x ≤ 50) the number of crashes is decreasing by 0.06 per additional thousand visits. O The coefficient 0.06 is the slope of the first formula, indicating that, for Web site traffic of up to 50,000 visits per day (0 ≤ x ≤ 50) the number of crashes is increasing by 0.06 per additional thousand visits. O The coefficient 0.06 is the intercept of the first formula, indicating that, if there were no visitors we would expect 0.06 crashes per day. O The coefficient 0.06 is the slope of the first formula, indicating that, for Web site traffic of up to 50 visits per day (0 ≤ x ≤ 50), the number of crashes is decreasing by 0.06 per additional visit. (c) Last Friday, the website went down ten times. Estimate the number of visits that day. visits
John O'Hagan is considering upgrading the Web server equipment at OHaganBooks.com because of frequent crashes. The tech services manager has been monitoring the frequency of crashes as a function of website traffic (measured in thousands of visits per day) and has obtained the following model c(x) = (0.06x + 2 0.08x + 1 if 0 ≤ x ≤ 50 if x > 50, where c(x) is the average number of crashes in a day in which there are x thousand visitors. (a) On average, how many times will the website crash on a day when there are 10,000 visits? times On average, how many times will the website crash on a day when there are 50,000 visits? times On average, how many times will the website crash on a day when there are 100,000 visits? times (b) What does the coefficient 0.06 tell you about the website's stability? The coefficient 0.06 is the slope of the first formula, indicating that, for Web site traffic of up to 50 visits per day (0 ≤ x ≤ 50), the number of crashes is increasing by 0.06 per additional visit. O The coefficient 0.06 is the slope of the first formula, indicating that, for Web site traffic of up to 50,000 visits per day (0 ≤ x ≤ 50) the number of crashes is decreasing by 0.06 per additional thousand visits. O The coefficient 0.06 is the slope of the first formula, indicating that, for Web site traffic of up to 50,000 visits per day (0 ≤ x ≤ 50) the number of crashes is increasing by 0.06 per additional thousand visits. O The coefficient 0.06 is the intercept of the first formula, indicating that, if there were no visitors we would expect 0.06 crashes per day. O The coefficient 0.06 is the slope of the first formula, indicating that, for Web site traffic of up to 50 visits per day (0 ≤ x ≤ 50), the number of crashes is decreasing by 0.06 per additional visit. (c) Last Friday, the website went down ten times. Estimate the number of visits that day. visits
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:John O'Hagan is considering upgrading the Web server equipment at OHagan Books.com because of frequent crashes. The tech services
manager has been monitoring the frequency of crashes as a function of website traffic (measured in thousands of visits per day) and has
obtained the following model
S0.06x + 2
c(x) =
0.08x + 1
if 0 ≤ x ≤ 50
if x > 50,
where c(x) is the average number of crashes in a day in which there are x thousand visitors.
(a) On average, how many times will the website crash on a day when there are 10,000 visits?
times
On average, how many times will the website crash on a day when there are 50,000 visits?
times
On average, how many times will the website crash on a day when there are 100,000 visits?
times
(b) What does the coefficient 0.06 tell you about the website's stability?
O The coefficient 0.06 is the slope of the first formula, indicating that, for Web site traffic of up to 50 visits per day (0 ≤ x ≤ 50), the
number of crashes is increasing by 0.06 per additional visit.
The coefficient 0.06 is the slope of the first formula, indicating that, for Web site traffic of up to 50,000 visits per day (0 ≤ x ≤ 50),
the number of crashes is decreasing by 0.06 per additional thousand visits.
O The coefficient 0.06 is the slope of the first formula, indicating that, for Web site traffic of up to 50,000 visits per day (0 ≤ x ≤ 50),
the number of crashes is increasing by 0.06 per additional thousand visits.
O The coefficient 0.06 is the intercept of the first formula, indicating that, if there were no visitors we would expect 0.06 crashes per
day.
O The coefficient 0.06 is the slope of the first formula, indicating that, for Web site traffic of up to 50 visits per day (0 ≤ x ≤ 50), the
number of crashes is decreasing by 0.06 per additional visit.
(c) Last Friday, the website went down ten times. Estimate the number of visits that day.
visits
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