In a PCR experiment, a 500 bp target is amplified starting with 1 copy of template DNA. If the efficiency of each cycle is 90 % (i.e., each cycle produces 0.9 new copies per existing copy), how many copies will be present after 30 cycles? Express your answer as a whole number of copies.

Step-by-step solution

1. Write the general formula for PCR amplification with efficiency e: Copies = initial × (1+e)^{n}.
2. Insert the values: initial = 1, e = 0.9, n = 30, so Copies = (1+0.9)^{30}=1.$9^{30}$.
3. Use logarithms or a calculator to evaluate 1.$9^{30}$.
4. Calculate $lo{g}_{10}$(1.$9^{30}$) = 30 × $lo{g}_{10}$(1.9) ≈ 30 × 0.2788 ≈ 8.364.
5. Convert back: $10^{8.364}$ ≈ 2.31 × $10^8$.
6. Since each successful cycle adds 0.9 new copies per existing copy, the exact number is 1.$9^{30}$ ≈ 1.98 × $10^9$ (rounded to nearest whole copy).

Concept tested: Quantitative PCR amplification

Published 20 September 2026 · How this solution was prepared and checked