An accident at a nuclear power plant has left the surrounding area polluted with radioactive material that decays naturally. The initial amount of radioactive material present is 15 su (safe units), and 5 months later it is still 10 su. dA dk A(t) and A(t) = A,ekt = dt a) Find the complete model that represents the amount, A(t), of radioactive material (in su) remaining after t months. Round k to 6 decimal places. b) What amount of radioactive material will remain after a year? Round your answer to the tenths place and use correct units. c) At what rate is the radioactive material decreasing after a year? Round your answer to the hundredths place and use correct units. d) The area is considered safe for humans when A = = 1 su. How many months will it take until the area is safe for people to return? Round your answer to the tenths place and use correct units.
An accident at a nuclear power plant has left the surrounding area polluted with radioactive material that decays naturally. The initial amount of radioactive material present is 15 su (safe units), and 5 months later it is still 10 su. dA dk A(t) and A(t) = A,ekt = dt a) Find the complete model that represents the amount, A(t), of radioactive material (in su) remaining after t months. Round k to 6 decimal places. b) What amount of radioactive material will remain after a year? Round your answer to the tenths place and use correct units. c) At what rate is the radioactive material decreasing after a year? Round your answer to the hundredths place and use correct units. d) The area is considered safe for humans when A = = 1 su. How many months will it take until the area is safe for people to return? Round your answer to the tenths place and use correct units.
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:An accident at a nuclear power plant has left the surrounding area
polluted with radioactive material that decays naturally. The initial
amount of radioactive material present is 15 su (safe units), and 5
months later it is still 10 su.
dAk A(t) and A(t)= A, ekt
=
dt
a) Find the complete model that represents the amount, A(t), of
radioactive material (in su) remaining after t months.
Round k to 6 decimal places.
b) What amount of radioactive material will remain after a year?
Round your answer to the tenths place and use correct units.
c) At what rate is the radioactive material decreasing after a year?
Round your answer to the hundredths place and use correct units.
d) The area is considered safe for humans when A= 1 su. How
many months will it take until the area is safe for people to
return?
Round your answer to the tenths place and use correct units.
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