Answer: it will take 18.2 years
Step-by-step explanation:
We would apply the formula,
y = ab^t
Where
a represents the initial amount of bacteria.
t represents the doubling.
From the information given
a = 10
t = 1 hour
Since after 1 hour, the amount of bacteria multiplies by 2, then
y = 2 × 10 = 20
Therefore
20 = 10 × b^1
Dividing through by 10, it becomes
2 = b
The equation becomes
y = 10(2)^t
For 3,000,000 bacteria, then
3000000 = 10(2)^t
3000000/10 = (2)^t
300000 = (2)^t
Taking log of both sides, it becomes
Log 300000 = tlog2
5.477 = 0.301t
t = 5.477/0.301
t = 18.2 years
