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.

Verified step by step guidance

1. Identify the given information: each square foot of plywood emits 140 micrograms of formaldehyde per hour, and the room has 100 square feet of plywood.
2. Calculate the total emission rate per hour by multiplying the emission rate per square foot by the total square footage: \(140 \times 100\) micrograms per hour.
3. Define the variable \(x\) as the number of hours.
4. Write the linear equation \(F(x)\) to represent the total amount of formaldehyde emitted after \(x\) hours by multiplying the total emission rate per hour by \(x\): \(F(x) = (140 \times 100) \times x\).
5. Simplify the equation if desired to express \(F(x)\) in terms of \(x\).

Key Concepts

Linear Equations

A linear equation represents a relationship between two variables with a constant rate of change, typically in the form y = mx + b. In this problem, the amount of formaldehyde emitted changes linearly over time, so the equation will model total emission as a function of hours.

Rate of Change (Slope)

The rate of change indicates how one quantity changes relative to another. Here, the emission rate per square foot per hour (140 μg/hr) is the slope, which must be multiplied by the total area and time to find total emissions.

Units and Dimensional Analysis

Understanding and correctly using units ensures the equation makes sense physically. Emission rate is given in micrograms per hour per square foot, so multiplying by area (square feet) and time (hours) yields total micrograms emitted.