Question

When concentrations of formaldehyde in the air exceed 33μg/ft³ (1μg=1 microgram =10⁻⁶ gram), a strong odor and irritation to the eyes often occurs. One square foot of hardwood plywood paneling can emit 3365μg of formaldehyde per day. A 5ft by 7ft sheet of paneling is attached to a wall in a room having floor dimensions of 10ft by 10ft and height of 7ft.

(a) The total area of hardwood plywood paneling is 35 ft² . If there is no ventilation in the room, write a linear equation that models the amount of formaldehyde F in the room after x days.

Answer 1

The linear equation that models the amount of formaldehyde F in micrograms in the room after x days is F = 117775x, assuming the room starts with no formaldehyde and there is no ventilation.

Step-by-step explanation:

To find a linear equation that models the amount of formaldehyde F in the room after x days, we will use the rate of emission of formaldehyde from the plywood paneling and the volume of the room. The total area of hardwood plywood paneling is 35 ft². Given that one square foot of hardwood plywood paneling can emit 3365μg of formaldehyde per day, the total emission per day for 35 ft² can be calculated by multiplying 3365μg by 35 ft².

So the total emission of formaldehyde per day = 3365μg/ft² × 35 ft² = 117775μg/day.

To write the equation, we assume that the room starts with no formaldehyde, so F will increase linearly by the amount of formaldehyde emitted per day. The linear equation modeling the total amount of formaldehyde after x days (F) can be represented as:

F = 117775x

Where:

• F is the total amount of formaldehyde in micrograms in the room after x days,
• x is the number of days after the plywood paneling is installed.