(A) Explanation The rate of increase in harmful bacteria t days after the treatment is given by d N d t = − 3 , 000 t 1 + t 2 , 0 ≤ t ≤ 10 . The minimum value of d N d t is calculated as follows. Differentiate both sides of the equation d N d t = − 3 , 000 t 1 + t 2 with respect to t . N ″ ( t ) = d d t ( − 3000 t 1 + t 2 ) = − 3 , 000 [ ( 1 + t 2 ) d d t ( t ) − t d d t ( 1 + t 2 ) ( 1 + t 2 ) 2 ] = − 3 , 000 [ ( 1 + t 2 ) ( 1 ) − t ( 2 t ) ( 1 + t 2 ) 2 ] = − 3 , 000 [ 1 + t 2 − 2 t 2 ( 1 + t 2 ) (B) To determine To find: The number of bacteria N ( t ) and the bacteria count after 5 days. (C) To determine To find: The number of days to become the bacteria counts 1,000 bacteria per milliliter.

Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)

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ISBN: 9780137400126

Author: Raymond Barnett, Michael Ziegler

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Chapter 5.2, Problem 87E

(A)

To determine

To find: The minimum value of dNdt.

(B)

To determine

To find: The number of bacteria N(t) and the bacteria count after 5 days.

(C)

To determine

To find: The number of days to become the bacteria counts 1,000 bacteria per milliliter.

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Chapter 5.2, Problem 86E

Chapter 5.2, Problem 88E

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Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)

Ch. 5.1 - Matched Problem 1 Note that ddx(x3)=3x2 A. Find...Ch. 5.1 - Find each indefinite integral: (A) 2dx (B) 16etdt...Ch. 5.1 - Matched Problem 3 Find each indefinite integral:...Ch. 5.1 - Matched Problem 4 Find the equation of the curve...Ch. 5.1 - Matched Problem 5 Find the revenue function R(x)...Ch. 5.1 - Matched Problem 6 There are currently 64,000...Ch. 5.1 - Explore and Discuss 1 Formulas 1, 2, and 3 do not...Ch. 5.1 - In Problems 18, write each function as a sum of...Ch. 5.1 - In Problems 18, write each function as a sum of...Ch. 5.1 - In Problems 18, write each function as a sum of...

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The minimum value of d N d t .

Solution Summary: The author calculates the minimum value of dNt, which is 1,500 bacteria/mL per day and the rate of increase in harmful bacteria t days after the treatment.

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To find: The minimum value of dNdt.

To find: The number of bacteria N(t) and the bacteria count after 5 days.

To find: The number of days to become the bacteria counts 1,000 bacteria per milliliter.

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Chapter 5 Solutions