dt' Population growth is commonly modeled upon the simple statement that the popu- lation growth rate, dy, is proportional to the present population, y. This can be written mathematically as = ay where a > 0. You have just purchased a piece of property with a small lake that is suitable for raising trout. You feel that without any aid from you the trout population introduced into the pond will grow at a nominal annual rate of 5%. You realize the resulting D.E. for the growth rate becomes dy = (1/20) y. dy dt 2. State an explicit solution to the D.E., dy dt = 2y with y(0) = 50. 20 3. Use the explicit solution to find the projected undisturbed trout population in the lake after 10 yrs, 30 yrs, 50 yrs, and 70 yrs. Give approximations to 2 decimal places.
dt' Population growth is commonly modeled upon the simple statement that the popu- lation growth rate, dy, is proportional to the present population, y. This can be written mathematically as = ay where a > 0. You have just purchased a piece of property with a small lake that is suitable for raising trout. You feel that without any aid from you the trout population introduced into the pond will grow at a nominal annual rate of 5%. You realize the resulting D.E. for the growth rate becomes dy = (1/20) y. dy dt 2. State an explicit solution to the D.E., dy dt = 2y with y(0) = 50. 20 3. Use the explicit solution to find the projected undisturbed trout population in the lake after 10 yrs, 30 yrs, 50 yrs, and 70 yrs. Give approximations to 2 decimal places.
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:dt'
Population growth is commonly modeled upon the simple statement that the popu-
lation growth rate, dy, is proportional to the present population, y. This can be written
mathematically as d = ay where a > 0. You have just purchased a piece of property
with a small lake that is suitable for raising trout. You feel that without any aid from
you the trout population introduced into the pond will grow at a nominal annual rate of
5%. You realize the resulting D.E. for the growth rate becomes dy = (1/20) y.
dy
dt
dt
2. State an explicit solution to the D.E.,
dt
-
1
20
y with y(0) = 50.
3. Use the explicit solution to find the projected undisturbed trout population in the
lake after 10 yrs, 30 yrs, 50 yrs, and 70 yrs. Give approximations to 2 decimal
places.
1
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