SME
Grade 9 Math · Problem type
Doubling time
Use this for “400 cells double every 3 hours. How many are there after 12 hours?”
Table
Hours passed (t)
Amount after time t (N)
This is an example. Type your own values to start a new problem.
N
=
N₀
(2)
/
k
Number of doublings
worked out (not typed)
Formulas
k
=
t
T
4
=
12
3
N
=
N₀
×
2
k
6,400
=
400
×
2
4
Assumptions
•
The amount doubles once every T time units, however large it is.
•
After time t it has doubled t ÷ T times, so multiply by 2 that many times.
•
Use the same time unit for t and T.
Step-by-step
WE KNOW
t = 12, N₀ = 400, T = 3
FIND
number of doublings (k), amount after time t (N)
Step 1 · Find number of doublings (k)
Use k = t ÷ T
Count the doublings: the time passed divided by the doubling time.
k
=
12
3
k
=
4
Step 2 · Find amount after time t (N)
Use N = N₀ × 2ᵏ
Multiply the starting amount by 2 once for each doubling.
N
=
400
×
2
4
N
=
400
×
16
N
=
6,400
Check
Put the numbers back in. Both sides should match.
4
=
12
3
✓
6,400
=
400
×
2
4
✓
Topic check
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