If the number of bacteria in a colony doubled every 207 min and there is currently a population of 1,500 bacteria what will the population be 621 minutes from now

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

12,000 bacteria

Step-by-step explanation:

621/207 = 3

therefor the bacteria will double 3 times

1500 x 2 = 3000

3000 x 2 = 6000

6000 x 2 = 12000