Digital SATMath: AlgebraEasy
A park ranger is monitoring the population of a certain species of bird. The population, P(t), after t years can be modeled by the equation P(t) = 1500 / (1 + 4e^(-0.5t)). What is the carrying capacity of this bird population?
- A1500
- B4
- C1 + 4e^(-0.5t)
- D0.5
Show answer & explanationAnswer & explanation
Correct answer: A. 1500
In a logistic growth model of the form P(t) = K / (1 + Ae^(-rt)), K represents the carrying capacity. In the given equation, 1500 is in the position of K.
Why the other options are wrong
- B. This value is part of the growth constant, not the carrying capacity.
- C. This is the denominator, which dictates how quickly the population approaches the carrying capacity, but is not the carrying capacity itself.
- D. This value represents the growth rate, not the carrying capacity.
Carrying Capacity (Logistic Growth)
The maximum population size of a biological species that can be sustained indefinitely by the environment, given the available resources.
- Represented by K in the logistic growth model P(t) = K / (1 + Ae^(-rt)).
- The population approaches this value as time (t) approaches infinity.
- It's a crucial concept in ecology and population dynamics.
Memory trick: K is the 'King' of the population, the ultimate limit.