A team of engineers is trying to pump out the air in a...

A team of engineers is trying to pump out the air in a vacuum chamber to lower the pressure. They know that the following equation represents the pressure in the chamber: $$ P=35-0.07 s $$ where $P$ is the pressure in pounds per square inch (psi) of the vacuum chamber and $s$ is the time in seconds. a. What will the pressure be after 150 seconds? b. When will the pressure inside the chamber be 1 psi?

A team of engineers is trying to pump out the air in a vacuum chamber to lower the pressure. They know that the following equation represents the pressure in the chamber:
$$
P=35-0.07 s
$$
where $P$ is the pressure in pounds per square inch (psi) of the vacuum chamber and $s$ is the time in seconds.
a. What will the pressure be after 150 seconds?
b. When will the pressure inside the chamber be 1 psi?

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Key Concepts

Linear Functions

A linear function is a mathematical expression that shows a constant rate of change with respect to its independent variable. It is typically represented in the form y = mx + b, where 'm' is the slope indicating how much y changes for each unit change in x, and 'b' is the y-intercept, the value of y when x is zero.

Slope-Intercept Form

The slope-intercept form of a linear equation, y = mx + b, clearly demonstrates both the rate of change (slope) and the initial value (y-intercept). This form is useful for quickly graphing the line and understanding the relationship between the variables.

Substitution in Functions

Substitution in functions involves replacing the variable in a function with a given value to calculate the corresponding value of the function. This process is fundamental in evaluating the function at specific points.

Solving Linear Equations

Solving linear equations entails isolating the variable on one side of the equation using algebraic manipulation, such as addition, subtraction, multiplication, or division. This process is crucial for finding unknown values that satisfy the equation.

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