Question

An ecologist at a wildlife refuge estimates that P, the population of pheasants at the refuge, can be modeled by the function P = s* (1.04)', where s is the starting population of pheasants and t is the number of years since the starting point.what is the correct change to describe the pheasants population? ​

Answer 1

The pheasant population is described as exponential growth at a rate of 4% per year. Starting with a base population 's', the population size 'P' increases to 's * (1.04)^t' after 't' years.

Step-by-step explanation:

The correct change to describe the pheasant population, as modeled by the function P = s * (1.04)^t, is exponential growth. In this model, s represents the starting population of pheasants, and t represents the number of years since the starting point. The factor 1.04 suggests that the population is expected to increase by 4% each year. This kind of growth is typical in ideal conditions where resources are not limited. However, in a real-world setting, factors such as food availability, disease, predators, and environmental changes can affect the pheasant population, leading to a more complex dynamic than simple exponential growth.

For example, if the starting population (s) is 100 pheasants, after one year (t = 1), the population would be P = 100 * (1.04)^1 = 104 pheasants. After two years (t = 2), it would be P = 100 * (1.04)^2 = 108.16 pheasants, and so on.