Final answer:
After five cycles of PCR, the number of amplified DNA pieces equals 2⁵, which represents exponential doubling after each cycle. This results in 32 molecules of the original DNA sequence.
Step-by-step explanation:
After five cycles of the Polymerase Chain Reaction (PCR), the number of amplified pieces of DNA is equal to 2⁵. PCR is a process designed to amplify DNA sequences exponentially. Starting with one DNA molecule, after one cycle of PCR, it will have doubled to two DNA molecules. After two cycles, those two molecules each double, resulting in four molecules. This doubling process continues for each cycle. Therefore, the equation for the number of DNA sequences after 'n' cycles is 2⁵.
A typical PCR might involve 30 cycles, resulting in nearly exponential amplification of the desired DNA sequence. In just a few hours, millions of copies of a targeted DNA sequence are made available, which are essential in many scientific and medical applications. For example, after 30 cycles, which is common in a PCR, we expect 2³⁰ double-stranded PCR products.