For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. ƒ(2)

Verified step by step guidance

1. Identify the function given: \( f(x) = 3^x \). We need to find \( f(2) \), which means substituting \( x = 2 \) into the function.
2. Substitute \( x = 2 \) into the function: \( f(2) = 3^{2} \).
3. Recall the exponent rule: \( a^{n} \) means multiplying the base \( a \) by itself \( n \) times. So, \( 3^{2} = 3 \times 3 \).
4. Calculate the value of \( 3^{2} \) by multiplying the base by itself the number of times indicated by the exponent.
5. Round the result to the nearest thousandth if necessary, as the problem instructs.

Key Concepts

Exponential Functions

Exponential functions have the form f(x) = a^x, where the base a is a positive constant. They model growth or decay processes and are evaluated by raising the base to the power of the input x. Understanding how to compute values for given x is essential.

Function Evaluation

Function evaluation involves substituting a specific input value into the function's formula and simplifying to find the output. For example, to find f(2), replace x with 2 and calculate the result.

Rounding to a Specified Decimal Place

Rounding is the process of limiting a number to a certain number of decimal places for simplicity or clarity. Here, answers should be rounded to the nearest thousandth, meaning three digits after the decimal point.