Which of the following behave according to a power model? Select all the apply.
1.Finance
2. Population
3. area
4. Pricing
5. volume
6. bacteria
7. mass
3 area = k L^2
5 volume = k L^3
7 mass = k L^3
for the others the increase tends to be a constant times the present value (like if every woman has two kids, the next generation will be twice the present one)
dF(t) = k F(t) d t
dF/F= k dt
ln F = k t + c
F = e^(kt+c) = C e^kt
Which means EXPONENTIAL MODEL not power model
To determine which entities behave according to a power model, it is necessary to understand what a power model means. In a power model, one variable is exponentially related to another variable.
Let's analyze each option to see if it aligns with a power model:
1. Finance: Finance is a broad term, and it does not specify a specific relationship between variables. Cannot determine if finance follows a power model without further information.
2. Population: The relationship between population and certain aspects, such as resource consumption or economic growth, can exhibit a power model. For example, the relationship between population and energy consumption generally follows a power model.
3. Area: The area refers to the size of a particular region or surface. In a power model, the relationship between variables is often characterized by exponential growth or decay. However, the area is generally not considered to have an exponential relationship with other variables but rather a linear relationship.
4. Pricing: Pricing typically does not follow a power model. Rather, it can be influenced by various factors such as supply and demand, production costs, and market competition. Therefore, pricing is unlikely to exhibit a power model.
5. Volume: In some cases, the relationship between the volume and other variables can be modeled using a power function. For example, in physics, the volume of a sphere or a cube is a function of the shape's dimensions, which demonstrates a power relationship.
6. Bacteria: The relationship between bacteria and variables such as growth rate or population count can exhibit a power model. Bacterial growth, such as exponential growth, can be described by a power function.
7. Mass: The relationship between mass and other variables is often linearly related or can follow specific equations such as Newton's laws of motion. It does not typically follow a power model.
Based on this analysis, the entities that may behave according to a power model are:
- Population
- Volume
- Bacteria
Please note that certain assumptions have been made to provide a general understanding. The behavior of these entities may vary based on specific contexts and circumstances.