Answer: 59 minutes
Step-by-step explanation:
We would apply the formula,
y = ab^t
Where
a represents the initial amount of bacteria.
t represents the doubling time.
From the information given
a = 10000000
t = 20 minutes
Since after 20 minutes, the population doubles, then
y = 2 × 10000000 = 20000000
Therefore
20000000 = 10000000 × b^20
2 = b^20
Raising both sides of the equation by 1/20, it becomes
2^(1/20) = b
The equation becomes
y = 10000000 × 2^(1/20)×t
y = 10000000 × 2^(t/20)
Therefore, the time it will take to get to 67 million microbes would be
67000000 = 10000000 × 2^(t/20)
67000000/10000000 = 2^(t/20)
6.7 = 2^(t/20)
6.7 = 2^(0.05t)
Taking log to base 10 of both sides, it becomes
Log 6.7 = 0.05t log 2
0.826 = 0.05t × 0.301
0.01505t = 0.826
t = 0.826/0.01505
t = 54.88
t = 59 minutes
