   Chapter 1.2, Problem 97E

Chapter
Section
Textbook Problem

Air Pollution Nitrogen dioxide is a brown gas that impairs breathing. The amount of nitrogen dioxide present in the atmosphere on a certain May day in the city of Long Beach measured in PSI (pollutant standard index) at time t, where t is measured in hours and t = 0 corresponds to 7 a.m., is approximated by 136 1 + 0.25 ( t − 4.5 ) 2 + 28 ( 0 ≤ t ≤ 11 ) Find the time of the day when the amount of nitrogen dioxide is greater than or equal to 128 PSI.Source: Los Angeles Times.

To determine
The time of the day when the amount of nitrogen dioxide is greater than or equal to the given value.

Explanation

Given:

The amount of nitrogen dioxide present in the atmosphere on a certain May day in the city of Long Beach measured in PSI at time t measured in hours and t=0 corresponds to 7 A.M is approximated by 1361+0.25(t4.5)2+28(0t11)

Calculation:

The expression for amount of nitrogen oxide greater than or equal to 128 PSI is expressed as,

1361+0.25(t4.5)2+28128

Solve the inequality to evaluate the interval of t.

1361+0.25(t4.5)2+281281361+0.25(t4.5)2100(Subtract28bothsides)136100(1+0.25(t4.5)2)(Crossmultiply)136100+25(t4.5)2[a(b+c)=ab+ac]

Simplify the expression and evaluate the value of t

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