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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

The table shows the number of people per day who died from SARS in Singapore at two-week intervals beginning on March 1, 2003.

Date Deaths per day
March 1 0.0079
March 15 0.0638
March 29 0.1944
April 12 0.4435
April 26 0.5620
May 10 0.4630
May 24 0.2897

(a) By using an argument similar to that in Example 4, estimate the number of people who died of SARS in Singapore between March 1 and May 24, 2003, using both left endpoints and right endpoints.

(b) How would you interpret the number of SARS deaths as an area under a curve?

Source: A. Gumel et al., “Modelling Strategies for Controlling SARS Outbreaks,” Proceedings of the Royal Society of London: Series B 271 (2004): 2223-32.

To determine

a)

To estimate:

The number of people who died of SARS in Singapore

Explanation

1) Concept:

Area under the graph is

A=limni=1nfxix

where,

x=b-an & xi=a+ix

2) Calculation:

Here,

x=14 days

So using left end points of each interval to estimate the total deaths in given time period,

L6=i=16fxix

=140

To determine

b)

To describe:

How to interpret the number of deaths as an area under a curve

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