Question

the population of locusts in a prairie a town overthe last 50 years is modelled by the functionthe locust population isgiven in hundreds of thousands. describe thelocust population in the town over time,where x is time in years.

Answer 1

The population of locusts in a town over the last 50 years can be modeled by a logistic function, where the locust population is given in hundreds of thousands and x represents time in years. The logistic model accounts for the fact that the locust population will eventually reach a carrying capacity, after which the growth rate slows down.

Step-by-step explanation:

The population of locusts in a town over the last 50 years can be modeled by a logistic function, where the locust population is given in hundreds of thousands and x represents time in years. The logistic model accounts for the fact that the locust population will eventually reach a carrying capacity, after which the growth rate slows down.

Let's say the logistic function is given by P(x) = C / (1 + a * e^(-b*x)), where P(x) represents the locust population at time x, C is the carrying capacity, a determines the initial growth rate, and b controls how quickly the growth rate slows down.

To describe the locust population over time, we need to know the values of C, a, and b. Without that information, we can't provide a precise description. However, we can explain the general behavior of the population based on the logistic model.

Initially, the population will experience rapid growth, approaching the carrying capacity. As the population approaches the carrying capacity, the growth rate will decrease, and eventually, the population will stabilize.