SME
Grade 9 Science · Problem type
PCR: copies double each cycle
Use this for “Starting from 2 copies, how many copies are there after 10 cycles of PCR?”
Diagram
2 × 2¹⁰ = 2,048
Each cycle doubles the copies.
This is an example. Type your own values to start a new problem.
N
=
N₀
×
2
Formulas
N
=
N₀
×
2
n
2,048
=
2
×
2
10
Assumptions
•
Each cycle heats the DNA to 95 °C to separate the strands, cools it to 55 °C so primers bind, and warms it to 72 °C to copy.
•
Every double strand is copied each cycle, so the copies double: N = N₀ × 2ⁿ.
•
Real runs level off after about 30 cycles, as the primers and nucleotides run low.
Step-by-step
WE KNOW
N₀ = 2, n = 10
FIND
copies after n cycles (N)
Step 1 · Find copies after n cycles (N)
Use N = N₀ × 2ⁿ
Each
cycle
doubles
the
copies:
n
doublings
of
N₀
.
N
=
2
×
2
10
N
=
2
×
1,024
N
=
2,048
Check
Put the numbers back in. Both sides should match.
2,048
=
2
×
2
10
✓
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