A colony starts with an initial number of 700 bacteria and d

A colony starts with an initial number of 700 bacteria, and doubles every day, how large is the colony after 7 days? (The bacteria lives a minimum of 10 days)

Solution

Initial number of bacterias = 700.

The number of bacteria doubles every day.

After 1 day, the number of bacterias = 700 x (2)¹

After 2 days, the number of bacterias = 700 x (2)²

And, similarly the number of bacterias will follow a geometric progression with the ratrio of 2.

The number of bacterias after a time of t days will be -

N = 700 x (2)^t

So, after 7 days the number of bacterias = 700 x (2)⁷ = 700 x 128 = 89600.

Hence there will be 89,600 bacterias after 7 days in the colony.