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
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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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