# A culture of bacteria doubles after 4 hours. If there are 8 g of bacteria to start with, how many are there after 8 hours and after 10 hours?

justaguide | College Teacher | (Level 2) Distinguished Educator

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The bacteria grow at an exponential rate. If there are n g to begin with, after 4 hours there are 2n g. The number of bacteria at any moment of time can be expressed as x(t) = x0*(2)^(t/4)

Initially the mass of the bacteria is 8 g, x0 = 8.

After 8 hours there would be 8*(2)^(8/4) = 8*2^2 = 8*4 = 32 gram.

After 10 hours there would be 8*2^(10/4) = 8*2^(2.5) = 45.25 g approximately.

After 8 hours we have 32 g of bacteria and after 10 hours we have 45.25 g of bacteria.

neela | High School Teacher | (Level 3) Valedictorian

Posted on

At the start there is 8 gm of bacteria.

Every 4 hours the growth rate is 2times

Every two hours the growth rate is sqrt2 times.

After 4 hrs, there are 8*2 = 16gm bacterias.

After 8th hour thereĀ  are 16*2 = 32 gm bacterias.

After another 2hours there should be 32*sqrt2 gmĀ  bacteria.