Final answer:
Operations of polynomials in creating new models include manipulation techniques, mathematical modeling, and algebraic expressions. Polynomial applications span across various real-life scenarios such as economic growth and disease spread. The term associated with using mathematical equations for ecosystems is 'analytical modeling'.
Step-by-step explanation:
Operations of polynomials can be used to create new polynomial models in various ways. These operations include polynomial manipulation techniques, which involve adding, subtracting, multiplying, and sometimes dividing polynomials to form new expressions that can model relationships and trends. For instance, if two factors affect a certain outcome and can be modelled as polynomials, their combined effect could be represented by the product of their respective polynomials.
Mathematical modelling with polynomials involves representing real-world situations using polynomial functions. For example, in physics, the trajectory of a projectile can be modelled by a quadratic function, which is a second-order polynomial. This is immensely helpful for making predictions about the path of the projectile under different conditions.
Algebraic expressions and functions are foundational in building polynomial models as they provide a formal language in which real-life phenomena can be succinctly expressed and analyzed. Practical applications of polynomials, or polynomial applications in real life, include fields such as economics, engineering, and biology. For instance, polynomials can help to model economic growth over time or the spread of a disease in epidemiology.
The term that describes the use of mathematical equations in the modelling of linear aspects of ecosystems is called analytical modelling. This approach simplifies complex systems into manageable parts that can be examined through algebraic expressions and functions.
In summary, the function of mathematics, and particularly polynomials, in modelling physical systems is indispensable for understanding complex relationships in an organized and simplified manner, enabling both prediction and analysis.