During a PCR, the efficiency per cycle is 92 %. Starting with 250 copies of a DNA fragment, how many copies will be present after 25 cycles? Express the answer in scientific notation (two significant figures).

medium 2 marks Class 12 · Biology · Biotechnology Principles and Processes

Answer

3.0 \times 1 0^{9}

copies

The correct answer is $3.0 \times 1 0^{9}$ copies — Round to two significant figures: 3.0× $1 0^{9}$ copies.

Step-by-step solution

Convert the efficiency to a multiplication factor: 100 % + 92 % = 1.92 per cycle.
Use the formula N = N₀ × (1.92)^{25}, where N₀ = 250.
Calculate (1.92)^{25} ≈ 1.21× $1 0^{7}$ (using a calculator or log10).
Multiply 250 × 1.21× $1 0^{7}$ = 3.02× $1 0^{9}$ .
Round to two significant figures: 3.0× $1 0^{9}$ copies.

Common mistake: Using 0.92 as the multiplication factor instead of 1.92

Concept tested: PCR amplification with less than 100 % efficiency