Digital SATMath: Advanced MathEasy
A biologist is studying a population of fruit flies. The population, P(t), after t days, can be modeled by the function P(t) = 500 / (1 + 4e^(-0.1t)). What is the maximum population the fruit fly colony can sustain?
- A500 flies
- B5,000 flies
- C100 flies
- D2,000 flies
Show answer & explanationAnswer & explanation
Correct answer: A. 500 flies
In a logistic growth model of the form P(t) = K / (1 + Ae^(-kt)), K represents the carrying capacity, which is the maximum sustainable population. In this equation, K = 500.
Why the other options are wrong
- B. This is a distracter, potentially from misinterpreting parts of the denominator or numerator.
- C. This is a distracter, potentially from incorrectly interpreting the '1' in the denominator.
- D. This is a distracter, potentially from multiplying 500 by 4.
Carrying Capacity
The maximum population size of a biological species that can be sustained indefinitely by the environment, given the available resources.
- Represented by 'K' in logistic growth models.
- It's the upper limit a population reaches.
- Determined by environmental factors like food, water, and space.
Memory trick: K is for 'Kapacity' – the top limit!