# Answer on Differential Equations Question for Elsie

Question #5211

Bacteria in a petrie dish double the area they cover everyday. If the dish is covered after 16 days, on what day was only one quarter of it covered?

Expert's answer

Let the area of the whole dish be 1.

Suppose the bacteria covered an area S

at the beginning.

After the first day it covered the area 2S, after the

second - 4S and so on.

So, after n days the bacteria covered (2^n)*S. We know

that after 16 days it covered the dish. We get:

(2^16)*S = 1, S =

1/(2^16) = 2^(-16).

Let x be the number of days that after x days only

one quarter was covered. Then

(2^x) * S = 1/4,

(2^x) * 2^(-16) =

2^(-2),

2^(x-16) = 2^(-2),

x - 16 = -2,

x = 14.

Suppose the bacteria covered an area S

at the beginning.

After the first day it covered the area 2S, after the

second - 4S and so on.

So, after n days the bacteria covered (2^n)*S. We know

that after 16 days it covered the dish. We get:

(2^16)*S = 1, S =

1/(2^16) = 2^(-16).

Let x be the number of days that after x days only

one quarter was covered. Then

(2^x) * S = 1/4,

(2^x) * 2^(-16) =

2^(-2),

2^(x-16) = 2^(-2),

x - 16 = -2,

x = 14.

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