Generalised logistic function
Okay kiddo, a generalised logistic function is like a toy box that can be used to model lots of different things, like how a certain fruit grows or how a population of animals changes over time.
Imagine you have a toy box, and you can put different toys inside it. If you put a ball inside, you can throw it up in the air and it will come back down. If you put a stuffed animal inside, you can hug it and play with it.
In the same way, a generalised logistic function can be used to model different things depending on what you put inside it. The function has three important parts: the starting point, the carrying capacity, and the growth rate.
The starting point is like the first toy you put into your toy box. It represents the starting value of what you want to model. For example, if you want to model how many apples you have in a basket, the starting point could be zero, because at the beginning you have no apples in the basket.
The carrying capacity is like the space inside your toy box. It represents the maximum value that your model can reach. For example, if you're modeling how many people can fit inside a building, the carrying capacity would be the maximum amount of people that can fit inside the building.
The growth rate is like the speed at which your toy box is filling up. It represents how quickly your model is changing over time. For example, if you're modeling how fast a plant is growing, the growth rate would represent how quickly the plant is getting bigger.
When you combine these three parts together in a generalised logistic function, you get a graph that looks like a hill. The bottom of the hill represents the starting point, and the top of the hill represents the carrying capacity. The curve of the hill represents how quickly your model is changing over time.
So, a generalised logistic function is like a toy box that can be used to model lots of different things. You can put different toys inside the toy box to represent the starting point, carrying capacity, and growth rate. When you put everything together, you get a graph that looks like a hill, which shows how your model is changing over time.
Imagine you have a toy box, and you can put different toys inside it. If you put a ball inside, you can throw it up in the air and it will come back down. If you put a stuffed animal inside, you can hug it and play with it.
In the same way, a generalised logistic function can be used to model different things depending on what you put inside it. The function has three important parts: the starting point, the carrying capacity, and the growth rate.
The starting point is like the first toy you put into your toy box. It represents the starting value of what you want to model. For example, if you want to model how many apples you have in a basket, the starting point could be zero, because at the beginning you have no apples in the basket.
The carrying capacity is like the space inside your toy box. It represents the maximum value that your model can reach. For example, if you're modeling how many people can fit inside a building, the carrying capacity would be the maximum amount of people that can fit inside the building.
The growth rate is like the speed at which your toy box is filling up. It represents how quickly your model is changing over time. For example, if you're modeling how fast a plant is growing, the growth rate would represent how quickly the plant is getting bigger.
When you combine these three parts together in a generalised logistic function, you get a graph that looks like a hill. The bottom of the hill represents the starting point, and the top of the hill represents the carrying capacity. The curve of the hill represents how quickly your model is changing over time.
So, a generalised logistic function is like a toy box that can be used to model lots of different things. You can put different toys inside the toy box to represent the starting point, carrying capacity, and growth rate. When you put everything together, you get a graph that looks like a hill, which shows how your model is changing over time.