Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Insert Draw Design Layout References Mailings X • Α' Α' 16 Euphemia... 11 B I U vab X₂ X² Po A A Aav Mathematical Investigation: Review ≡≡≡ v a) State the initial population. P(t) = 200- 20(0) (0)² P(0) = 200 Hence, the initial population is 200. View PART A: Tell me 2↓ ¶ The population p, in thousands of bacterial colonies on a kitchen bench can be modelled by the function p(t) = 200 + 20t - t2 where t is time in hours. AaBbCcDdE. AaBbCcDdE Aa BbCcDc AaBbCcDdE Aa Bb Normal No Spacing Heading 1 Heading 2 b) Determine the growth rate of the population in terms of t. d P' (t) (200 + 20t-t²) dt P'(t)20-2t c) What does it mean when p'(t) = 0? Calculate the value of t when this occurs and explain what this answer means. P'(t) = 0 ⇒ 20-2t = 0 ⇒ t = 10 Hence, it means that at point t=10 the bacteria's stop growing. d) Explain what happens to p'(t) for t greater than the value you found in part c. Give one reason why this might occur. Title
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Transcribed Image Text:Insert Draw Design Layout References Mailings X • Α' Α' 16 Euphemia... 11 B I U vab X₂ X² Po A A Aav Mathematical Investigation: Review ≡≡≡ v a) State the initial population. P(t) = 200- 20(0) (0)² P(0) = 200 Hence, the initial population is 200. View PART A: Tell me 2↓ ¶ The population p, in thousands of bacterial colonies on a kitchen bench can be modelled by the function p(t) = 200 + 20t - t2 where t is time in hours. AaBbCcDdE. AaBbCcDdE Aa BbCcDc AaBbCcDdE Aa Bb Normal No Spacing Heading 1 Heading 2 b) Determine the growth rate of the population in terms of t. d P' (t) (200 + 20t-t²) dt P'(t)20-2t c) What does it mean when p'(t) = 0? Calculate the value of t when this occurs and explain what this answer means. P'(t) = 0 ⇒ 20-2t = 0 ⇒ t = 10 Hence, it means that at point t=10 the bacteria's stop growing. d) Explain what happens to p'(t) for t greater than the value you found in part c. Give one reason why this might occur. Title
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