Understanding Exponential Functions: Exploring the Equation y = 2^x and its Applications

y= 2^x

exponential parent function

The equation y = 2^x represents an exponential function. In this equation, x is the exponent, and 2 is the base.

To understand how this function works, you can evaluate different values of x to find their corresponding y-values. Let’s take some examples:

When x = 0:
y = 2^0
y = 1

When x = 1:
y = 2^1
y = 2

When x = 2:
y = 2^2
y = 4

When x = -1:
y = 2^-1
y = 1/2

Based on this pattern, you can see that as x increases, the value of y also increases exponentially. The function y = 2^x represents a curve that continuously grows steeper and steeper as x becomes larger. Similarly, when x is negative, the curve assumes decreasing values.

It’s important to note that exponential functions have many real-world applications, such as economic growth, population growth, and radioactive decay. They can be used to model situations where there is constant multiplication or division of a quantity over time.

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