A nonlinear relationship is when two things you’re comparing don’t increase or decrease at a steady rate. In other words, if you make a graph of the relationship, it won’t form a straight line like linear relationships—it will curve, bend, or take another shape. For example, if you double the speed of a car, the stopping distance doesn’t just double, it grows much more, which is a nonlinear effect.
Examples of Nonlinear Relationships
- 1. Balloon Volume vs Radius
- 2. Amount of Exercise vs Weight loss
- 3. Amount of a Radioactive Element Remaining vs Time
- 4. Height of sea tides vs time
- 5. Geometric Relationship
- 6. Relating Area and the Side of a Square
- 7. Charging a capacitor
- 8. Relating Pressure and Volume of a Gas
- 9. Relating the Area of A Circle and Radius
- 10. Relating Energy of a Moving Object and Its Velocity
1. Balloon Volume vs Radius
If you inflate a balloon and take data of its radiuses at various volume levels, you will get a nonlinear relationship. This is also described as a cubic relationship.
2. Amount of Exercise vs Weight loss
It is often believed that the more effort one puts into working out, the more one should lose weight. However, this may not hold. Sometimes, doubling your exercise may not lead to an equivalent reducing effect on weight.
3. Amount of a Radioactive Element Remaining vs Time
How long will it take for a given amount of uranium to deplete? This can be modeled by getting data on the mass of the matters left and the time elapsed. The result is a non-linear relationship between the variables
4. Height of sea tides vs time
If we plot the heights of the low and high tide of the sea and relate it with time, it produces a nonlinear relationship. This is called a cyclic or periodic relationship because its curve has a repetitive sequential shape. The curve uses trigonometry (sine and cosine) to model this relationship.
5. Geometric Relationship
Geometric relationships are ones where you produce a geometric sequence such as 1, 8,27, 64… If we take our independent variables of 1, 2, 3 and order them with the dependent variables of 8,27, 64…it will reveal a nonlinear relationship.
6. Relating Area and the Side of a Square
If you take the side of your square as the independent variable X and area Y as the dependent variable, we can plot your data which will obtain a curve showing a nonlinear relationship. The relationship will be found to be a quadratic relationship rather than a linear one.
7. Charging a capacitor
A capacitor is a device that stores energy. After discharging, it needs to be recharged. What kind of relationship holds between the charge and the time it takes to charge?
You can plot the data and investigate. It will be found that the charge and time have a nonlinear relationship. For example, the charge does not double after two seconds compared to what its level was after one second.
8. Relating Pressure and Volume of a Gas
If you vary the pressure of a gas in a container and compare it to the volume, you will get a nonlinear relationship.
9. Relating the Area of A Circle and Radius
When you relate the area of a circle to its radius, it will give you a nonlinear relationship. The resulting curve will show a quadratic relationship with radius as the independent variable and the area of the dependent variable.
10. Relating Energy of a Moving Object and Its Velocity
How much energy does an object have due to its motion? If you plot the energy that a body has against the velocity, you get a nonlinear relationship. This is represented as a curve on a graph that is quadratic in nature.