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In 2003 at the outbreak of the SARS epidemic on April 1 there were 1084 cases. On April 15 there were 1952 cases. Assuming that the number of cases is an exponential function f(x) = Ab" where x is the number of days after April 1, find A and b. Use your model to estimate the number of cases on April 20. By what percentage is the number of cases incressing per day?

In 2003 at the outbreak of the SARS epidemic on April 1 there were 1084 cases. On April 15 there were 1952 cases. Assuming that the number of cases is an exponential function f(x) = Ab" where x is the number of days after April 1, find A and b. Use your model to estimate the number of cases on April 20. By what percentage is the number of cases incressing per day?

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 2ECP
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In 2003 at the outbreak of the SARS epidemic on April 1 there were 1084 cases. On April 15 there were 1952 cases. ASsuming that the number of cases is an exponential function f(x) = Ab* where x is the number of days after April 1, find A and b. Use your model to estimate the number of cases on April 20. By what percentage is the number of cases incressing per day?
Transcribed Image Text:In 2003 at the outbreak of the SARS epidemic on April 1 there were 1084 cases. On April 15 there were 1952 cases. ASsuming that the number of cases is an exponential function f(x) = Ab* where x is the number of days after April 1, find A and b. Use your model to estimate the number of cases on April 20. By what percentage is the number of cases incressing per day?
Expert Solution
Step 1: Introduction

At April 1, x=0

      f(x)=Abxf(x=0)=Ab0    1084=A

At April 15, x=14

      f(x)=Abxf(x=14)=1084b14    1952=1084b14          b=1.0429

So, the function is   f(x)=1084(1.0429)x

At April 20, x=19

f(x)=1084(1.0429)x=10841.042919=2407.90≈2408

There will be approximately 2408 cases on April 20. 

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