SME
Grade 9 Science · Problem type
Doubling time
Use this for “Bacteria double every 15 minutes. How many are there after 2 hours, starting from 40?”
Chart
N(6) = 6,400
Time: 120 min
Doubling time: 20 min
This is an example. Type your own values to start a new problem.
N
=
N₀
×
2
min
/
min
g
Doublings
worked out (not typed)
Formulas
g
=
t
d
6
=
120
20
N
=
N₀
×
2
g
6,400
=
100
×
2
6
Assumptions
•
With plenty of food and space, a population doubles every doubling time d: exponential growth.
•
After t minutes it has doubled g = t ÷ d times, so N = N₀ × 2ᵍ.
•
Real populations slow down as food runs out; this is the early, exponential part.
Step-by-step
WE KNOW
N₀ = 100, d = 20 min, t = 120 min
FIND
doublings (g), population after t (N)
Step 1 · Find doublings (g)
Use g = t ÷ d
How many doubling times fit into the time.
g
=
120
20
g
=
6
Step 2 · Find population after t (N)
Use N = N₀ × 2ᵍ
Each
doubling
multiplies
the
population
by
2:
g
doublings
multiply
it
by
2ᵍ.
N
=
100
×
2
6
N
=
100
×
64
N
=
6,400
Check
Put the numbers back in. Both sides should match.
6
=
120
20
✓
6,400
=
100
×
2
6
✓
Topic check
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