For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.A scientist is studying the effectiveness of 2 different antibiotics on the same strain of bacteria. He uses the same dose of each antibiotic and starts with the same initial bacteria count, in billions, in each petri dish. His results are shown in the tables below. Let x represent the time in hours.Antibiotic A: f(x)=1.5(0.56)x123450.84 billion0.47 billion0.263 billion0.148 billion0.083 billionAntibiotic B: g(x)=1.5(0.48)x123450.72 billion0.346 billion0.166 billion0.08 billion0.038 billionPart A: What is the initial number of bacteria in each petri dish? Explain your answer.Part B: What is the decay rate for each antibiotic? Explain your answer.Part C: How many bacteria will be left in each petri dish after the time has reached 8 hours? Round to the nearest thousandth. Show your work.

Answered: Antibiotic A: f(x)=1.5(0.56)x 1 2 3 4…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.

A scientist is studying the effectiveness of 2 different antibiotics on the same strain of bacteria. He uses the same dose of each antibiotic and starts with the same initial bacteria count, in billions, in each petri dish. His results are shown in the tables below. Let x represent the time in hours.

Antibiotic A: f(x)=1.5(0.56)x
1	2	3	4	5
0.84 billion	0.47 billion	0.263 billion	0.148 billion	0.083 billion

Antibiotic B: g(x)=1.5(0.48)x
1	2	3	4	5
0.72 billion	0.346 billion	0.166 billion	0.08 billion	0.038 billion

Part A: What is the initial number of bacteria in each petri dish? Explain your answer.

Part B: What is the decay rate for each antibiotic? Explain your answer.

Part C: How many bacteria will be left in each petri dish after the time has reached 8 hours? Round to the nearest thousandth. Show your work.

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