Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 6500. The number of fish grew to 700 in the first year. a)Find an equation for the number of fish P(t) after t years P(t) = b) How long will it take for the population to increase to 3250 (half of the carrying capacity)? It will take years.
Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 6500. The number of fish grew to 700 in the first year. a)Find an equation for the number of fish P(t) after t years P(t) = b) How long will it take for the population to increase to 3250 (half of the carrying capacity)? It will take years.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population for the
fish of that species in that lake) to be 6500. The number of fish grew to 700 in the first year.
a)Find an equation for the number of fish P(t) after t years
P(t) =
b) How long will it take for the population to increase to 3250 (half of the carrying capacity)?
It will take
years.
Transcribed Image Text:Suppose a student carrying a flu virus returns to an isolated college campus of 1000 students. After 5 days,
54 students have been infected with the virus. The rate at which the virus spreads is proportional to the
product of the number P(t) of infected students and the number of students not infected.
Write the initial value problem. When writing the differential equation, use a capital P for the number of
students infected, and k for the constant of proportionality.
dP
kP(1000 – P)
O P(0)
1
dt
Determine the number of infected students after 1 weeks. Round to the nearest student.
infected students
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