The intensity of light I (measured in luxes (lx)) at depth y (in m) below the surface of a lake can be modelled by the differential equation dī -kI (I>0, y ≥ 0) dy where k is a positive constant. (b) (a) Find the general solution of this differential equation in explicit form. The intensity of light at the surface of the lake is 1800 lx. Find the particular solution that describes the intensity of light as a function of depth below the surface of the lake. (c) The intensity of light is 300 lx at 10 m below the surface of the lake. Use this fact to find the value of the constant k. Give both its exact value and its value to two significant figures. (d) Use your particular solution and the exact value of k to find the intensity of light 17 m below the surface of the lake. Give your answer in luxes to two significant figures. (e) Use Maxima to find the solution of the initial value problem dI -kI, where I(0) = 1800 dy Include a screenshot or printout of your Maxima worksheet in your answer. = =
The intensity of light I (measured in luxes (lx)) at depth y (in m) below the surface of a lake can be modelled by the differential equation dī -kI (I>0, y ≥ 0) dy where k is a positive constant. (b) (a) Find the general solution of this differential equation in explicit form. The intensity of light at the surface of the lake is 1800 lx. Find the particular solution that describes the intensity of light as a function of depth below the surface of the lake. (c) The intensity of light is 300 lx at 10 m below the surface of the lake. Use this fact to find the value of the constant k. Give both its exact value and its value to two significant figures. (d) Use your particular solution and the exact value of k to find the intensity of light 17 m below the surface of the lake. Give your answer in luxes to two significant figures. (e) Use Maxima to find the solution of the initial value problem dI -kI, where I(0) = 1800 dy Include a screenshot or printout of your Maxima worksheet in your answer. = =
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:The intensity of light I (measured in luxes (lx)) at depth y (in m) below the
surface of a lake can be modelled by the differential equation
dī
-kI (I>0, y ≥ 0)
dy
where k is a positive constant.
(b)
(a) Find the general solution of this differential equation in explicit form.
The intensity of light at the surface of the lake is 1800 lx. Find the
particular solution that describes the intensity of light as a function of
depth below the surface of the lake.
(c) The intensity of light is 300 lx at 10 m below the surface of the lake.
Use this fact to find the value of the constant k. Give both its exact
value and its value to two significant figures.
(d) Use your particular solution and the exact value of k to find the
intensity of light 17 m below the surface of the lake. Give your answer
in luxes to two significant figures.
(e) Use Maxima to find the solution of the initial value problem
dI
-kI, where I(0) = 1800
dy
Include a screenshot or printout of your Maxima worksheet in your
answer.
=
=
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