   Chapter 10.5, Problem 89E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

The 2003 SARS Outbreak In the early stages of the SARS (severe acute respiratory syndrome) epidemic in 2003, the number of reported cases could be approximated by A ( t ) = 167 ( 1.18 ) t      ( 0 ≤ t ≤ 20 ) t days after March 17,2003 (the first day in which statistics were reported by the World Health Organization.)a. What, approximately, was the instantaneous rate of change of A ( t )   on March  27 ( t = 10 ) ? Interpret the result.b. Which of the following is true? For the first 20 days of the epidemic, the instantaneous rate of change of the number of cases(A) increased. (B) decreased.(C) increased and then decreased.(D) decreased and then increased.

(a)

To determine

To calculate: The instantaneous rate of change of the number of case reported on March 27 and explain it, if the number of cases reported in the early stages of SARS by WHO that is represented by A(t)=167(1.18)t 0t20

Explanation

Given information:

The number of cases of SARS reported by WHO is represented by A(t)=167(1.18)t where 0t20, t represents the number of days after 17 March 2003

Formula used:

The instantaneous rate of change is the derivative of the function, which is given by the rule

limΔx0ΔfΔx

Where Δf can be determined using the balance difference quotient of a function f(x) at any point a defined by the rule

f(a)f(a+h)f(ah)2h

Where, the value of h=0.0001.

Calculation:

Consider the number of cases reported of SARS, A(t)=167(1.18)t

Evaluate instantaneous rate of change using balance difference quotient at t=10

A(a)A(a+h)A(ah)2h

Evaluate the instantaneous rate of change at t=10

A(10)A(10+0.001)A(100.0001)2(0.0001)A(10)A(10

(b)

To determine

The correct option for the instantaneous rate of change of number of new cases of SARS reported by WHO for first 20 days if the number of cases of SARS reported by WHO is represented by A(t)=167(1.18)t here 0t20.

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