Final answer:
The function b(x) = 13(0.7)^x is an exponential function representing exponential decay due to its base (0.7) being less than one. Exponential functions can be manipulated using properties of natural exponents and logarithms to solve various mathematical problems pertaining to growth and decay.
Step-by-step explanation:
The exponential function described by b(x) = 13(0.7)^x is a type of mathematical expression characterized by a constant raised to a power that is a variable. In this particular function, 0.7 is the base and x is the exponent, which means as x increases, the function will decrease since 0.7 is less than 1. This decreasing pattern reflects exponential decay. The concept of the exponential function is essential for understanding various growth and decay processes in mathematics.
Using Exponential Functions
To solve different kinds of exponential equations, we can employ methods as indicated by Eq. 1.1 and Eq. 1.2. For instance, by recognizing that an exponential function can be expressed in terms of the natural base e (≈ 2.7183) using logarithms, as shown in M = b = e^(n ln(b)). This technique is useful for transforming a problem into a more solvable form by utilizing properties of the natural exponent and logarithms.