Answer: the population would be 11085 in 621 minutes from now
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 = 1500
t = 207 minutes
Since after 207 minutes, the amount of bacteria doubles, then
y = 2 × 1500 = 3000
Therefore
3000 = 1500 × b^207
Dividing through by 1500, it becomes
2 = b^207
Taking log of both sides of the equation, it becomes
Log 2 = 207 log b
0.301 = 207 log b
Log b = 0.301/207 = 0.00145
Taking inverse log of both sides of the equation, it becomes
10^logb = 10^ 0.00145
b = 1.00334
The equation becomes
y = 1500(1.00334)^t
When t = 621 minutes, the population would be
y = 1500(1.00334)^621
y = 11085
