The fission reactor of a nuclear plant explodes at t = 0. The following function d represents the density in radioactive particles per metre cubed in the air inside the plant, as a function of t in hours: d(t) = te¹0-t. It is deemed safe to enter the nuclear plant as soon as d is below 4. = (a) Suppose we used Newton's Method with an initial guess of t₁ 10 to find an approximation for the time when the density of the radioactive particles equals zero. Would Newton's Method ever find a time when the radioactive particle density equals zero? Explain. (b) Use L'Hospital's Rule to show that the density of radioactive particles tends to zero in the long run. (c) Compute the third degree Taylor polynomial, T3 (t), of the function d(t) at t = 10. (d) Use T3(t) to approximate the value of d(10+). (Round your answer to two decimal places.) Assuming that this approximation is good enough, is it safe to enter the nuclear plant after (10+) hours? Explain.
The fission reactor of a nuclear plant explodes at t = 0. The following function d represents the density in radioactive particles per metre cubed in the air inside the plant, as a function of t in hours: d(t) = te¹0-t. It is deemed safe to enter the nuclear plant as soon as d is below 4. = (a) Suppose we used Newton's Method with an initial guess of t₁ 10 to find an approximation for the time when the density of the radioactive particles equals zero. Would Newton's Method ever find a time when the radioactive particle density equals zero? Explain. (b) Use L'Hospital's Rule to show that the density of radioactive particles tends to zero in the long run. (c) Compute the third degree Taylor polynomial, T3 (t), of the function d(t) at t = 10. (d) Use T3(t) to approximate the value of d(10+). (Round your answer to two decimal places.) Assuming that this approximation is good enough, is it safe to enter the nuclear plant after (10+) hours? Explain.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:1. The fission reactor of a nuclear plant explodes at t = 0. The following function d represents the density
in radioactive particles per metre cubed in the air inside the plant, as a function of t in hours:
d(t) = te¹0-t.
It is deemed safe to enter the nuclear plant as soon as d is below 4.
=
(a) Suppose we used Newton's Method with an initial guess of t₁ 10 to find an approximation for
the time when the density of the radioactive particles equals zero. Would Newton's Method ever
find a time when the radioactive particle density equals zero? Explain.
(b) Use L'Hospital's Rule to show that the density of radioactive particles tends to zero in the long run.
(c) Compute the third degree Taylor polynomial, T3 (t), of the function d(t) at t = 10.
(d) Use Të(t) to approximate the value of d(10 + ģ). (Round your answer to two decimal places.)
Assuming that this approximation is good enough, is it safe to enter the nuclear plant after
(10+) hours? Explain.
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Follow-up Question
part d)
Use T3(t) to approximate the value of d(10 + b/6 ). (Round your answer to two decimal places.)
Assuming that this approximation is good enough, is it safe to enter the nuclear plant after
(10 + b/6 ) hours? Explain.
b=8
Solution
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