Homework Help is Here – Start Your Trial Now!
Math
Algebra
A population of bacteria, B, can be modeled using the exponential function B (x) = 3 (2)“ , wherez is the number of days since the population was first observed. Which domain is most appropriate to use to determine the population over the course of the first week? Ax 0 B0

A population of bacteria, B, can be modeled using the exponential function B (x) = 3 (2)“ , wherez is the number of days since the population was first observed. Which domain is most appropriate to use to determine the population over the course of the first week? Ax 0 B0

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question
100%
### Understanding Exponential Growth in Bacterial Populations In this educational example, we will explore how a population of bacteria can be modeled using an exponential function. The scenario and question presented are as follows: --- **Scenario:** A population of bacteria, denoted by \( B(x) \), can be modeled using the exponential function: \[ B(x) = 3 \cdot (2)^x \] where \( x \) is the number of days since the population was first observed. --- **Question:** Which domain is most appropriate to use to determine the population over the course of the first week? - **A)** \( x \geq 0 \) - **B)** \( 0 \leq x \leq 7 \) - **C)** \( 0 \leq x \leq 1 \) - **D)** \( x \leq 2 \) --- **Explanation:** To determine the appropriate domain, we need to consider the time frame specified in the question: "the first week." A week consists of 7 days. Therefore, we need a domain for \( x \) that includes the start of the observation (day 0) and extends up to day 7. - **Option A \( (x \geq 0) \)** includes all days starting from day 0, but it does not specify an upper limit. It extends beyond one week. - **Option B \( (0 \leq x \leq 7) \)** specifies a range from day 0 to day 7, which perfectly aligns with the first week. - **Option C \( (0 \leq x \leq 1) \)** only includes the first day, which is insufficient for observing the population over the entire first week. - **Option D \( (x \leq 2) \)** limits the days observed to 2 days, which again, is insufficient for the whole week. Thus, the correct answer is: **B) \( 0 \leq x \leq 7 \)**. This domain ensures that we are observing the bacterial population throughout the entire first week.
Transcribed Image Text:### Understanding Exponential Growth in Bacterial Populations In this educational example, we will explore how a population of bacteria can be modeled using an exponential function. The scenario and question presented are as follows: --- **Scenario:** A population of bacteria, denoted by \( B(x) \), can be modeled using the exponential function: \[ B(x) = 3 \cdot (2)^x \] where \( x \) is the number of days since the population was first observed. --- **Question:** Which domain is most appropriate to use to determine the population over the course of the first week? - **A)** \( x \geq 0 \) - **B)** \( 0 \leq x \leq 7 \) - **C)** \( 0 \leq x \leq 1 \) - **D)** \( x \leq 2 \) --- **Explanation:** To determine the appropriate domain, we need to consider the time frame specified in the question: "the first week." A week consists of 7 days. Therefore, we need a domain for \( x \) that includes the start of the observation (day 0) and extends up to day 7. - **Option A \( (x \geq 0) \)** includes all days starting from day 0, but it does not specify an upper limit. It extends beyond one week. - **Option B \( (0 \leq x \leq 7) \)** specifies a range from day 0 to day 7, which perfectly aligns with the first week. - **Option C \( (0 \leq x \leq 1) \)** only includes the first day, which is insufficient for observing the population over the entire first week. - **Option D \( (x \leq 2) \)** limits the days observed to 2 days, which again, is insufficient for the whole week. Thus, the correct answer is: **B) \( 0 \leq x \leq 7 \)**. This domain ensures that we are observing the bacterial population throughout the entire first week.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Transcendental Expression
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS