ACT (Enhanced)MathematicsMedium
A biologist is observing a population of bacteria that grows according to the logistic model P(t) = 1000 / (1 + 9e^(-0.5t)), where P(t) is the population at time t in hours. What is the carrying capacity of this bacterial population?
- A9
- B9000
- C1000
- D100
Show answer & explanationAnswer & explanation
Correct answer: C. 1000
In a logistic growth model of the form P(t) = K / (1 + Ae^(-kt)), the carrying capacity (K) is the numerator of the fraction.
Why the other options are wrong
- A. This is the initial growth factor 'A' in the denominator, not the carrying capacity.
- B. This would incorrectly multiply the initial factor by the numerator, not a parameter of the model.
- D. This is an arbitrary value and does not correspond to a parameter in the logistic model.
Logistic Growth Model
A mathematical model describing population growth that is limited by a carrying capacity, resulting in an S-shaped curve.
- P(t) = K / (1 + Ae^(-kt)) is the standard form.
- K represents the carrying capacity (maximum population).
- As t approaches infinity, P(t) approaches K.
Memory trick: Logistic's K: the ceiling, the limit, the carrying capacity's feeling.