Understanding Exponential Functions | An Overview of the Math Behind Growth and Decay

f(x) = 1(3)^x

The function f(x) = 1(3)^x represents an exponential function

The function f(x) = 1(3)^x represents an exponential function.

In this case, the base of the exponential function is 3, and the function is multiplied by a coefficient of 1. The parameter x represents the input or independent variable of the function, and f(x) represents the output or dependent variable.

To evaluate the function, you would substitute a specific value for x and calculate the corresponding value of f(x). For example, if x = 2, then f(2) = 1(3)^2 = 1(9) = 9. This means that when x = 2, the output of the function is 9.

The exponential function 3^x represents repeated multiplication of the base (in this case 3) by itself x times. As x increases, the value of the function grows rapidly since each multiplication by 3 increases the result exponentially. Conversely, as x decreases, the value of the function gets smaller, approaching zero but never actually reaching it.

Exponential functions are commonly used to model quantities that grow or decay exponentially over time, such as population growth, compound interest, radioactive decay, etc. They have many applications in various fields including finance, biology, physics, and economics.

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