State whether each function is increasing, decreasing, or neit...

Question

State whether each function is increasing, decreasing, or neither.

c. Height above Earth’s sea level as a function of atmospheric pressure (assumed nonzero)

Accepted Answer

Welcome back, everyone. Is the following function increasing, decreasing, or neither? Volume of a gas as a function of applied pressure, assuming temperature remains constant. For this problem, we need some context, and we essentially need to understand boils law from chemistry. This is really important to describe this function mathematically. So now Boy's law says that volume of a gas is inversely proportional to applied pressure at a constant temperature, and we can basically express this equation as V equals constant k divided by P, where V is volume and P is pressure, so we can define this function as V of P equals some constant k. Divided by P. Now P is the independent variable, right? And V is our dependent variable. As we can see this function describes inverse proportionality. Between B and B. And we can simply recall that whenever we are observing an inverse proportionality, this means that with an increase in the independent variable. The dependent variable decreases. So basically we have a hyperbolic function, right? Essentially, we can recall that this is very similar to a function Y equals K divided by X, which is a hyperbole. So with an increase in the denominator, The fraction itself decreases, assuming that K is constant. Therefore, the final answer to this problem is decreasing. Simply speaking, with an increase in the applied pressure, the volume of a gas decreases, and that's our final answer. Thank you for watching.

State whether each function is increasing, decreasing, or neither.

c. Height above Earth’s sea level as a function of atmospheric pressure (assumed nonzero)

Key Concepts

Monotonic Functions

Derivative and Its Sign

Inverse Relationships

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