   Chapter 2.2, Problem 83E 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 six months of the 2014 Ebola outbreak, the total number of reported cases was increasing at a continuous rate of about 72% per month.22 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 predict the number of cases as of August 1, 2014. (The actual number of reported cases was 1,603.) [HINT: See Example 5.]

To determine

To calculate: The exponential model of the Ebola outbreak in the form of C(t)=Aert

(after t months after April 1, 2014) and to predict the number of cases as of 1 August 2014 if there were 100 cases as of April 2014 and it increases continuously at the rate of 72% per month.

Explanation

Given Information:

There were 100 cases as of April 2014 and it increases continuously at the rate of 72% per month.

Formula used:

The formula for exponential model is,

C(t)=Aert

Here, t is the time in months after 1 April 2014.

The property of exponentials is, b0=1

Calculation:

Convert the rate of interest in the decimal form.

r=72%=72100=0.72

Consider the exponential model.

C(t)=Aert

Since there were 100 cases as of April 2014 and it increases continuously at the rate of 72% per month.

Substitute C(t)=100 and t=0 in the expression C(t)=Aert.

100=Aer(0)100=Ae0Ae0=100

Use the formula b0=1 to solve further,

Ae0=100A=100

Thus substitute A=100 and r=0

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