Understanding Exponential Growth | Evaluating a Function with a Given Value

f(x) = 2(3)^x

Sure, I can help you with that

Sure, I can help you with that.

Let’s break down the given function:
f(x) = 2(3)^x

In this function, we have the variable x, and we need to find the value of f(x) for a given value of x.

To evaluate the function, we substitute the value of x into the function and perform the necessary calculations.

For example, if we were asked to find f(2), we would substitute x = 2 into the function:
f(2) = 2(3)^2.

Now we solve the expression within the parentheses first, which is 3^2 = 3 * 3 = 9.

Substituting this value back into the function, we have:
f(2) = 2(9).

Finally, we multiply 2 by 9:
f(2) = 18.

Therefore, when x = 2, f(x) equals 18.

In general, the function f(x) = 2(3)^x represents exponential growth. The base of the exponential function is 3, and the coefficient 2 determines the initial value or the starting point. As x increases, the output of the function grows rapidly due to the exponentiation.

More Answers:
Understanding Exponential Growth in the Mathematical Function f(x) = 0.5 * (4)^x
Exponential Functions Explained | Evaluating and Graphing with Examples
Understanding the Chain Rule | Finding the Derivative of e^x Using the Chain Rule

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