If the exponential function is f(x) = 2^x, what is f(3)?

To find the value of the exponential function ( f(x) = 2^x ) at ( x = 3 ), we substitute 3 into the function. This gives us:

[ f(3) = 2^3 ]

Calculating ( 2^3 ):

• ( 2^1 = 2 )
• ( 2^2 = 4 )
• ( 2^3 = 2 \times 2 \times 2 = 8 )

So, ( f(3) = 8 ), which confirms that the value of the function when ( x = 3 ) is indeed 8.

This understanding of how exponential functions operate is crucial, as it illustrates how to evaluate them for any input value. In this case, recognizing that ( 2^3 ) is simply ( 2 ) multiplied by itself three times leads us directly to the answer.