In a favorable habitat and without natural predators, a population of reindeer is introduced to an island preserve. The reindeer is introduced, F(t), t as the year after their introduction is modeled by the poly function F(x)=-0.125t^5+3.125+4000.
1. What is used to model relationships of variables?
2. What's the use of having the accurate graph of the polynomial function?
1. To model relationships of variables, mathematical functions are often used. A function is a rule that assigns one unique output value (dependent variable) to each input value (independent variable). Functions can represent various relationships between variables, such as linear, exponential, polynomial, or trigonometric relationships. In this case, the relationship between the number of years after the reindeer introduction (t) and the population of reindeer (F(t)) is modeled using a polynomial function.
2. Having an accurate graph of the polynomial function allows us to visualize the relationship between the number of years and the population of reindeer. The graph provides a visual representation of how the population changes over time. It helps us understand the trend and behavior of the population, such as whether it is increasing or decreasing, and at what rate. Additionally, by analyzing the graph, we can make predictions about future population trends and estimate important points, such as the maximum population reached or when the population might reach certain thresholds. Therefore, the accurate graph of the polynomial function provides valuable insights and helps us better understand and study the reindeer population dynamics on the island preserve.