A researcher sets up a polymerase chain reaction (PCR) starting with 4 copies of a specific target gene. At the end of the amplification process, the tube contains 1024 copies of the gene. Assuming 100% efficiency in every cycle, how many cycles of PCR were completed?

Step-by-step solution

The amplification of DNA during PCR follows an exponential growth pattern described by the equation: Final number of copies = Initial number of copies 2^n where n is the number of cycles. Given: Initial copies = 4 Final copies = 1024 Substituting the values: 1024 = 4 2^n 2^n = 1024 4 2^n = 256 Since 2^8 = 256 , the number of cycles n = 8 . Choosing 10 is a mistake resulting from ignoring the initial 4 copies and assuming 2¹⁰ = 1024 . Choosing 16 is a mistake from incorrectly taking the square root of 256 instead of