Advances in medical science and healthier lifestyles have...

Advances in medical science and healthier lifestyles have resulted in longer life expectancies. The life expectancy of a male whose current age is $x$ years old is $$\begin{array}{ll}f(x)=0.0069502 x^{2}-1.6357 x+93.76 & (60 \leq x \leq 75)\end{array}$$ years. What is the life expectancy of a male whose current age is $65 ?$ A male whose current age is $75 ?$

Advances in medical science and healthier lifestyles have resulted in longer life expectancies. The life expectancy of a male whose current age is $x$ years old is
$$\begin{array}{ll}f(x)=0.0069502 x^{2}-1.6357 x+93.76 & (60 \leq x \leq 75)\end{array}$$
years. What is the life expectancy of a male whose current age is $65 ?$ A male whose current age is $75 ?$

Key Concepts

Domain Restrictions

Domain restrictions define the set of values for which a function is applicable or valid. They are important to consider in mathematical functions to ensure the inputs lead to meaningful and accurate outputs, especially when the model is intended to represent real-world phenomena within a specific range.

Mathematical Modeling

Mathematical modeling involves formulating real-world scenarios using mathematical expressions or functions. It allows for the analysis and prediction of behaviors, such as estimating life expectancy changes over time. This process is critical in sciences and engineering for making informed decisions based on quantitative data.

Quadratic Functions

Quadratic functions are polynomial functions where the highest power of the variable is two. They have a general form of ax² + bx + c and are used to describe parabolic trends. Understanding their properties, such as the vertex, axis of symmetry, and the effect of varying coefficients, is essential in many fields of study, including physics and economics.

Function Evaluation

Function evaluation refers to the process of substituting a specific value for the variable in a function to calculate a corresponding output. This process is fundamental in mathematics as it allows one to determine the behavior or result of the function at particular inputs, and it is especially crucial when working with modeling functions.

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