Suppose the population P of rainbow trout in a fish hatchery is modeled by the differential equation where P is measured in thousands of trout and t is measured in years. Suppose P(0) = 1. (a) How many trout are initially in the hatchery? trout. (b) Find a formula for the population at any time. P(t) = thousands of trout. (c) What is the size of the trout population after a very long time? lim P(t) = thousands of trout. 00+7 (d) At what time is the trout population increasing most rapidly? t = years. dP = P(6 - P), dt
Suppose the population P of rainbow trout in a fish hatchery is modeled by the differential equation where P is measured in thousands of trout and t is measured in years. Suppose P(0) = 1. (a) How many trout are initially in the hatchery? trout. (b) Find a formula for the population at any time. P(t) = thousands of trout. (c) What is the size of the trout population after a very long time? lim P(t) = thousands of trout. 00+7 (d) At what time is the trout population increasing most rapidly? t = years. dP = P(6 - P), dt
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:Suppose the population P of rainbow trout in a fish hatchery is modeled by the differential equation
where P is measured in thousands of trout and t is measured in years. Suppose P(0) = 1.
(a) How many trout are initially in the hatchery?
trout.
(b) Find a formula for the population at any time.
P(t)
=
thousands of trout.
(c) What is the size of the trout population after a very long time?
lim P(t) =
thousands of trout.
00+7
(d) At what time is the trout population increasing most rapidly?
t =
years.
dP
= P(6 - P),
dt
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