What mathematical expression represents the total number of colors based on the number of bits per pixel?

The total number of colors that can be represented based on the number of bits per pixel is expressed by the formula ( 2^n ), where ( n ) is the number of bits. Each bit can have two possible values: 0 or 1. Therefore, for each additional bit added, the number of possible combinations—and consequently, the number of different colors that can be represented—doubles.

For example, if there is 1 bit per pixel, there are ( 2^1 = 2 ) colors. If there are 2 bits per pixel, there are ( 2^2 = 4 ) colors. Generally, with ( n ) bits, the total combinations are ( 2^n ), allowing for a rapid increase in color variability with just a few additional bits.

The other answers do not accurately represent the relationship between the number of bits and the number of colors. Options like ( n^2 ) suggest that colors could be represented in a quadratic manner, which does not capture the binary nature of bits. ( n! ) represents the factorial of ( n ), which relates to permutations, not color representations. Lastly, ( 3*n ) implies a linear