Exploring Exponential Growth | Understanding the Math Behind the Function f(x) = 2^x

f(x)=2^x

The function f(x) = 2^x represents exponential growth

The function f(x) = 2^x represents exponential growth. In this function, the base of the exponential is 2, and the exponent is x.

To understand this function better, let’s evaluate it for different values of x:

For x = 0:
f(0) = 2^0 = 1
Any number raised to the power of 0 is always 1. So, when x is 0, the function evaluates to 1.

For x = 1:
f(1) = 2^1 = 2
When x is 1, the function evaluates to 2, as 2^1 = 2.

For x = 2:
f(2) = 2^2 = 4
At x = 2, the function evaluates to 4, since 2 raised to the power of 2 equals 4.

For x = -1:
f(-1) = 2^(-1) = 1/2
When x is -1, the function evaluates to 1/2, as 2^(-1) is equal to 1 divided by 2, which is 1/2.

The function f(x) = 2^x grows exponentially as x increases. As x approaches positive infinity, the function approaches infinity. This means that the values of f(x) get larger and larger as x increases.

Conversely, as x approaches negative infinity, the function approaches 0. As x becomes more negative, the values of f(x) get closer and closer to 0.

Overall, the function f(x) = 2^x represents exponential growth with a base of 2, where the values of f(x) increase rapidly as x increases.

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