   Chapter 10.4, Problem 49E 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 2014 Ebola Outbreak In the first 6 months of the 2014 Ebola outbreak, the total number of reported cases could be approximated by C ( t ) = 95.0 e 0.72 t     ( 0 ≤ t ≤ 6 ) Where t is time in months since April 1, 2014.51a. Calculating the average rate of change of C ( t ) over the successive 2-mont periods [ 0 , 2 ] , [ 1 , 3 ] , [ 2 , 4 ] , [ 3 , 5 ] , and [ 4 , 6 ] . (Round answers to two decimal places.)b. What kind of model would best describe the successive rates of change obtained in part (a): linear, quadratic, or exponential? What does your answer tell you about the 2014 Ebola outbreak?

(a)

To determine

To calculate: The average rates of change of C(t)

over the two-month periods [ 0,2 ],[ 1,3 ],[ 2,4 ],[ 3,5 ],[ 4,6 ]

if the total number of cases of Ebola is given by the equation C(t)=95.9e0.72t

(0t6)

where t is time in months since April 1,2014.

Explanation

Given Information:

The total number of cases of Ebola is given by the equation C(t)=95.9e0.72t

(0t6)

where t is time in months since April 1,2014

and the intervals are [ 0,2 ],[ 1,3 ],[ 2,4 ],[ 3,5 ],[ 4,6 ].

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 that the total number of cases of Ebola is given by the equation C(t)=95.9e0.72t

(0t6)

where t is time in months since April 1,2014

and the intervals are [ 0,2 ],[ 1,3 ],[ 2,4 ],[ 3,5 ],[ 4,6 ].

Now, apply the average rate of change formula for the interval [ 0,2 ]:

Average rate of change of C=C(2)C(0)20

Now, try to find C(2) and C(0):

Now, substitute the value 2

in the function:

C(2)=95.9e0.72(2)=95.9e1.44=404.765

Now, substitute the value 0

in the function:

C(0)=95.9e0.72(0)=95.9e0=95.9

Substitute the values in the equation,

C(2)C(0)20=404.76595.92=308.8652154.43 cases per month

Now, apply the average rate of change formula for the interval [ 1,3 ]:

Average rate of change of C=C(3)C(1)31

Now, find C(3) and C(1):

Substitute the value 1

in the function:

C(1)=95.9e0.72(1)=95.9e0.72=197.020

Substitute the value 3

in the function:

C(3)=95.9e0.72(3)=95.9e2.16=831.562

Substitute the values in the equation,

C(3)C(1)31=831.562197.0202=634

(b)

To determine

The model that would best describe the successive rates of change obtained in part (a)

and to explain what the answer says about the Ebola outbreak if the total number of cases of Ebola is given by the equation C(t)=95.9e0.72t

(0t6)

where t is time in months since April 1,2014.

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