Power Functions With Fractional Exponents For Non-Linear Modeling.

Power Function with fractional exponents

Normal line to a Curve C at a Point P is the line through P that is perpendicular to the tangent line at P

A power function is a mathematical expression of the form y=x^a, where x is the independent variable, y is the dependent variable, and ‘a’ is a constant exponent. When the exponent ‘a’ is a positive fraction, the function is called a power function with fractional exponents.

The power function with fractional exponents is defined for all real values of the independent variable ‘x’. The key feature of a power function with fractional exponents is that it allows us to calculate the nth root of a number, where ‘n’ is the denominator of the fractional exponent.

For example, the power function y = x^(3/2) can be used to calculate the square root of x, where x is a positive number. To find the square root of a number using this power function, we simply plug in the value of ‘x’ into the expression and evaluate it. For instance, if x=16, then we have that y = 16^(3/2) = 64.

One important thing to note is that power functions with fractional exponents have some specific properties that differ from whole number exponents. For instance, when the exponent is negative in a fractional power function, the function is undefined for zero values and positive values of the independent variable.

Another thing to remember is that power functions with fractional exponents are non-linear functions, because they involve raising the independent variable to a non-integer power. This means that the slope of the function changes at different points along the curve, making it a useful tool in modeling real-world data where non-linear relationships are present.

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