# How can carrying capacity affect populations?

Carrying capacity effectively determines how much population a given region can support. It will act as an upper limit on the population size.

In general, however, for purposes of a logistic growth model, one can consider the carrying capacity to be an asymptote for the logistic growth function. Specifically in the case of a constant carrying capacity, if one's independent variable (time usually, though sometimes resources or the like) is on the "x" axis, and one's dependent variable (in this case, population) is on the "y" axis, the carrying capacity will be a horizontal asymptote parallel to the x-axis, and will represent a population level that the growth model will typically not reach.

Of note is that certain drastic circumstances can push a population over the carrying capacity (one of the more common examples being the sudden introduction of a large number of new specimens of the population). In these cases, the population tends to rapidly decrease, plunging back below the carrying capacity (and in many cases, even decreasing below the original number).

By signing up, you agree to our Terms of Service and Privacy Policy

Carrying capacity affects populations by determining the maximum number of individuals of a particular species that an environment can support over a long period without causing environmental degradation. When a population exceeds its carrying capacity, it leads to resource depletion, increased competition for those resources, poorer health and survival rates, and eventually a population decline as the environment can no longer sustain the oversized population. Conversely, if a population is below its carrying capacity, it typically experiences better growth and survival rates until it approaches the carrying capacity limit.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the volume of the solid produced by revolving #f(x)=x^3-2x+3, x in [0,1] #around the x-axis?
- If a particular integral of the differential equation #(D^2+2D-1)y=e^(ax)# is #(-4/7)e^(ax)# then the value of a is ?
- What is a solution to the differential equation #dy/dx=x^2y#?
- What is the effect of exponential growth on a population?
- How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #x=y^2#, #y=0#, and #y=sqr2# rotated about the x axis?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7