As observed on earth, a certain type of bacteria is known to double in number ev

Question

As observed on earth, a certain type of bacteria is known to double in number every 16 hours. Two cultures of these bacteria are prepared, each consisting initially of one bacterium. One culture is left on earth and the other placed on a rocket that travels at a speed of 0.680c relative to the earth. At a time when the earthbound culture has grown to 512 bacteria, how many bacteria are in the culture on the rocket, according to an earth-based observer?
11. Chapter 28, Problem 07 As observed on earth, a certain type of bacteria is known to double in number every 16 hours. Two cultures of these bacteria are prepared, each consisting initially of one bacterium. One culture is left on earth and the other placed on a rocket that travels at a speed of 0.680c relative to the earth. At a time when the earthbound culture has grown to 512 bacteria, how many bacteria are in the culture on the rocket, according to an earth-based observer? Units Number

Explanation / Answer

Here, the amount of bacteria after a certain time the bacteria has existed is given by

A=(2)(t/16)

where A = initial amount of bacteria

t =time in hours.

here, A is one in this case for both cultures. because time for the rocket is equal to time on earth times

(1 - v2/c2)1/2

Putting V = 0.680 , we get

(1 - 0.6802)1/2

0.733

thus, the amount of bacteria in the rocket is equal to

A = 2(0.733t/16)

where t is the time it took for 512 bacteria to develop which comes to be

5120.733

this gives

(2(t/16))0.733

as 2(t/16) = 512 and this is equal to 5120.733

96.8 or approx to 97 bacteria

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