   Chapter 10.4, Problem 48E 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 A few weeks into the SARS (severe acute respiratory syndrome) epidemic in 2003, the number of reported cases could be approximated by A ( t ) = 1 , 804 ( 1.04 ) t     ( 0 ≤ t ≤ 30 ) t days after March 17, 2003a. What was the average rate of change of A ( t ) fromAprill 19 ( t = 18 ) toAprill 29? Interpret the result.b. Which of the following is true? For the first 30 days period beginning Aprill 1, the number of reported cases(A) increased at a faster and faster rate.(B) increased at a slower and slower rate.(C) decreased at a faster and faster rate.(D) decreased at a slower and slower rate. [HINT: See Example 2.]

(a)

To determine

To calculate: The average rate of change of the function A(t) from April 19 to April 29, if the number of SARS report in 2003 is provided as a function with respect to days A(t)=1804(1.04)t where (0t30).

Explanation

Given Information:

The provided period is April 19 to April 29 and the provided function is A(t)=1804(1.04)t where (0t30).

Formula used:

Average rate of change of f(x) over the interval [a,b] is:

Average rate of change of f=Change in fChange in x=ΔfΔx=f(b)f(a)ba

Calculation:

Consider the function A(t)=1804(1.04)t where (0t30), The period is from April 19 to April 29.

So, the corresponding interval of this period is [18,28].

Now, apply the average rate of change formula:

Average rate of change of A=A(28)A(18)2818

Compute the value of A(18) and A(28):

Now, substitute the value 18 in the function:

A(18)=1804(1

(b)

To determine

The correct option of the number of report cases for the first average rates of change from 30 days period, if the provided options are:

(A) Increased at a faster and faster rate.

(B) Increased at a slower and slower rate.

(C) Decreased at a faster and faster rate.

(D) Decreased at a slower and slower rate.

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