Solve each problem. See Examples 5 and 6. Formaldehyde is an i...

Question

Solve each problem. See Examples 5 and 6. Formaldehyde is an indoor air pollutant formerly found in plywood, foam insulation, and carpeting. When concentrations in the air reach 33 micrograms per cubic foot (μg/ft³), eye irritation can occur. One square foot of new plywood could emit 140 μg per hr. (Data from A. Hines, Indoor Air Quality & Control.) A room has 100 ft² of new plywood flooring. Find a linear equation F that computes the amount of formaldehyde, in micrograms, emitted in x hours.

Accepted Answer

Hello, today we're going to be solving the following word problem. So we are told that a new material was used on a wall of a room and this material is known to release toxic particles. The particles can cause sneezing if the concentration in the air reaches 900 micrograms per cubic meter, one square meter of this material could release the particles at a rate of 100 and 20 micrograms per hour. And the room has a total amount of 80 m squared of wall. We want to write a linear equation which represents the amount of particles released an X amount of hours. So let's go ahead and make a sense of the information that's given to us. So we are told that one square meter of this new material releases the particles at a rate of 120 micrograms per hour. And again, we are told that the room has total of 80 m squared of wall. So in order to write a linear equation P which represents the amount of particles released in an unknown amount of hours, we're gonna multiply the 120 micrograms per hour per meter squared. So we're going to write 100 20 micrograms per hour per meter squared. And this represents the rate of particles released by only one m square of wall. And since there is a total amount of 80 m squared of wall, we're going to multiply this value by 80 m squared. And finally, since we don't know the amount of hours that this is going to be in the room, we're going to multiply this by X amount of hours. So multiplying this together the units hours and meters squared are going to cancel out, which only leaves us with micrograms. And what we are left with is 120 times times x micrograms and 100 and times 80 is going to give us micrograms or 9600 times X micrograms. And this is going to be the equation that represents the amount of micrograms released per hour. And with that being said, the answer to this problem is going to be a so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Key Concepts

Linear Equations

Rate of Change (Slope)

Units and Dimensional Analysis

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