The time, t, in weeks, needed for the population of fireflies in a field to reach p individuals is given by: t(p)=45ln(10000/18000-p') 10000< or equal p < 18000 What is the population of fireflies after 5 weeks?
The time, t, in weeks, needed for the population of fireflies in a field to reach p individuals is given by: t(p)=45ln(10000/18000-p') 10000< or equal p < 18000 What is the population of fireflies after 5 weeks?
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section: Chapter Questions
Problem 33CT
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The time, t, in weeks, needed for the population of fireflies in a field to reach p individuals is given by:
t(p)=45ln(10000/18000-p')
10000< or equal p < 18000
What is the population of fireflies after 5 weeks?
Expert Solution
Step 1
t(p)=45ln[10,000/(18,000-p)]
We have to find the population, p when t = 5
Step 2
t = 45ln[10,000/(18,000-p)]
Hence, ln[10,000/(18,000-p)] = t/45
Or, 10,000 / (18,000 - P) = et/45
Or, (18,000 - P) / 10,000 = e-t/45
Hence, P = 18,000 -10,000e-t/45
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