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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
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.

(a)

To determine

To calculate:

The amount of people died from SARS between March 1 and May 24, 2003 using left endpoints.

The amount of people died from SARS between March 1 and May 24, 2003 using right endpoints.

Explanation

Given information:

The amount of people died from SARS is tabulated at two weeks interval. Hence, the value of Δt is 14 days.

The number of intervals as n=6.

Calculation:

Show the expression to calculate the number of persons died from SARS in the country using left endpoints:

Ln=f(t0)Δt+f(t1)Δt+...+f(tn1)Δt (1)

Here, the deaths per day at time t0 is f(t0), the deaths per day at time t1 is f(t1), and the deaths per day at time tn1 is f(tn1).

Substitute 6 for n, 0.0079 for f(t0), 0.0638 for f(t1), 0.1944 for f(t2), 0.4435 for f(t3), 0.5620 for f(t4), and 0.4630 for f(t5) in Equation (1).

L6=[(0.0079×14)+(0.0638×14)+(0.1944×14)+(0.4435×14)+(0.5620×14)+(0.4630×14)]=0.1106+0.8932+2.7216+6.2090+7

(b)

To determine

To interpret: The amount of SARS death as an area under a curve.

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