Final answer:
Proportional relationships involve two variables that maintain a constant ratio to each other, such as the direct proportionality between income and number of alumni calls made in a fundraising job. Inverse proportionality is seen in scenarios like a car's fuel efficiency in relation to speed. Understanding these constants of proportionality is crucial in fields like economics and biology.
Step-by-step explanation:
A proportional relationship is an equation wherein one variable is directly proportional to another or inversely proportional to another. For example, if you're paid %2.50 for each alumni call you make in a university fund-raising job, you have a direct proportional relationship between your income (p) and the number of calls (n), expressed as p = 2.50 x n. The more calls you make, the more money you earn, maintaining a consistent ratio.
Conversely, an inverse proportional relationship is seen in cases like a car that consumes less fuel the slower it travels, represented by y = k/x, where y might be fuel efficiency and x your speed. The constant k represents the specific fuel efficiency at a given speed.
In both scenarios, you're looking at the constants of proportionality; in fundraising, it's the rate per call, and in fuel efficiency, it's the car's efficiency at a certain speed. Understanding these relationships helps in various fields, from economics (Law of Variable Proportion) to biology (exponential bacterial growth rates).