Explanation 1) Approach: The theoretical statement can be converted into a mathematical statement by assuming some variable for the unknowns in the statement and by applying suitable algebraic method, the value of the unknown in the statement can be obtained. 2) Calculation: Given, The count in a culture of bacteria was 400 after 2 hours and 25600 after 6 hours. Here, After 2 hour the count in culture of bacteria is 400. (i.e.) n ( 2 ) = 400 . After 6 hours the count in culture of bacteria is 25600. (i.e.) n ( 6 ) = 25600 Since, the exponential form of population growth after time t . n ( t ) = n 0 e r t There, we take n ( 2 ) = 400 is the initial population. n ( 6 ) = 25600 is the population after 4 hours, (i.e.) n 0 = 400 , t = 4 and n ( 4 ) = 25 , 600 Now, find r , 25600 = 400 e r ( 4 ) 25600 = 400 e 4 r To determine b) To find: The initial size of the culture. To determine c) To find: The function that model the number of bacteria n ( t ) after t hours. To determine d) To find: The number of bacteria after 4.5 hours. To determine e) To find: The number of hours that after the number of bacteria reach 50, 000.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 4.6, Problem 14E

To determine

a) To find:

The relative rate of growth of the bacteria population, and express in percentage.

To determine

b) To find:

The initial size of the culture.

To determine

c) To find:

The function that model the number of bacteria n(t) after t hours.

To determine

d) To find:

The number of bacteria after 4.5 hours.

To determine

e) To find:

The number of hours that after the number of bacteria reach 50, 000.

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Chapter 4.6, Problem 13E

Chapter 4.6, Problem 15E

Chapter 4 Solutions

Algebra and Trigonometry (MindTap Course List)

Ch. 4.1 - The function f(x)=5x is an exponential function...Ch. 4.1 - Prob. 2E Ch. 4.1 - a To obtain the graph of g(x)=2x1, we start with...Ch. 4.1 - In the formula A(t)=P(1+rn)nt for compound...Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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a) To find: The relative rate of growth of the bacteria population, and express in percentage.

Solution Summary: The author explains how the theoretical statement can be converted into a mathematical statement by assuming some variable for the unknowns in the statement and applying suitable algebraic method.

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a) To find: The relative rate of growth of the bacteria population, and express in percentage.

b) To find: The initial size of the culture.

c) To find: The function that model the number of bacteria n(t) after t hours.

d) To find: The number of bacteria after 4.5 hours.

e) To find: The number of hours that after the number of bacteria reach 50, 000.

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Chapter 4 Solutions

a) To find:

The relative rate of growth of the bacteria population, and express in percentage.

b) To find:

The initial size of the culture.

c) To find:

The function that model the number of bacteria n(t) after t hours.

d) To find:

The number of bacteria after 4.5 hours.

e) To find:

The number of hours that after the number of bacteria reach 50, 000.