According to a recent data analysis, the amount A(t) of atmospheric pollutants in a certain city is found to approximately quadruple every 9.5 years. The current amount of pollution in this city is 25 pu (pollutant units), and it is considered to be dangerous to stay in the city when the amount of pollutants reaches 120 pu. Applying the differential equation model: (dA/dt) = kA. (k>0) approximately, how long do the residents of this city have before the dangerous limit is reached? Choose All Correct Answers Below (A) 10.75 years B) 13.64 years C) 12.3 years D) 8.45 years (E) 11.85 years (F) 9.53 years

According to a recent data analysis, the amount A(t) of atmospheric pollutants in a certain city is found to approximately quadruple every 9.5 years. The current amount of pollution in this city is 25 pu (pollutant units), and it is considered to be dangerous to stay in the city when the amount of pollutants reaches 120 pu. Applying the differential equation model: (dA/dt) = kA. (k>0) approximately, how long do the residents of this city have before the dangerous limit is reached? Choose All Correct Answers Below (A) 10.75 years B) 13.64 years C) 12.3 years D) 8.45 years (E) 11.85 years (F) 9.53 years

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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Question

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According to a recent data analysis, the amount A(t) of atmospheric pollutants in a certain city is found to approximately
quadruple every 9.5 years. The current amount of pollution in this city is 25 pu (pollutant units), and it is considered to be
dangerous to stay in the city when the amount of pollutants reaches 120 pu.
Applying the differential equation model: (dA/dt) = kA, (k>0)
approximately, how long do the residents of this city have before the dangerous limit is reached?
Choose All Correct Answers Below
A
B
E
10.75 years
13.64 years
12.3 years
8.45 years
11.85 years
9.53 years

Expert Solution

Step 1

Given ,

The current pollutants is Po=25 pu

Quadruple for every 9.5 years

so, Q=9.5

Using the formula

$P(t) = P.(4) ) (4) =$

Put values

$P(t) = 25(4) 5$

now, we can set P(t)=120

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