   Chapter 11.5, Problem 95E 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 was increasing exponentially with a monthly growth constant of 72%.There were about 100 cases as of April 1, 2014. Find an exponential model in the form C ( t ) = A e r t for the number of cases t months after April 1, 2014, and use it to estimate how fast the number of cases was increasing on August 1, 2014. (Round your answer to the nearest 10 new cases per month.)

To determine

To calculate: The exponential model in the form of C(t)=Aert that predicts the number of people infected t days after April 1,2014 and then to estimate the rate at which Ebola was growing on August 1,2014 if it is given that the number of cases was increasing by 72% per month and on April 1,2014, there were 100 cases of Ebola.

Explanation

Given Information:

The number of cases was increasing by 72% per month and on April 1,2014, there were 100 cases of Ebola.

Formula used:

The exponential model is given by the following formula:

C(t)=Aert

Where

A= Initial casesr= Rate of increaset=Time

The following derivative formula is used:

ddx(ex)=ex

Where ‘a’ is any constant

Calculation:

Consider that the number of cases was increasing by 72% per month and on April 1,2014, there were 100 cases of Ebola.

Consider the formula, C(t)=Aert

At t=0 (April 1,2014) the number of cases was 100

So, A=100

The number of cases was increasing by 72% per month.

So,

r=0

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