From the following information, calculate the average mass of a single bacterium.
A newly discovered strain of bacteria divides once every 60 minutes under ideal conditions. After 24 hours, a single bacterium produces cells that have a mass of 1 kilogram.
Please explain how you got your answer. Thanks!
The short answer to your question is that each bacterium must weigh 5.96 x 10^-5 grams.
The way to get this is by using a formula for exponential growth. The formula is
y = a(1+r)^x
In this formula, y is your ending quantity. A is your beginning quantity. R is the rate of increase. X is the number of times that increase occurs.
R is usually expressed as a decimal, so in this case it is 1 because the rate of increase is 100%.
So your equation will be
y = 1(1+1)^24 or y = 2^24 which is equal to 16,777,216.
To get the weight of each bactermium, divide 1000 grams by the number of bacteria.
As the bacteria divides every 60 minutes or every 1 hour, the number of bacteria doubles every 1 hour. Thus a single bacterium will increase to 2 bacteria after 1 hour, which will further double to 4 bacteria after 2 hours and 8 bacteria after 3 hours. Thus we can represent the number of bacteria (N) after h hours by the formula:
N = 2^h
Number of bacteria after 24 hours = 2^24 = 16777216
It is given mass of bacteria after 24 hours is 1 kilogram.
Average mass of a single bacterium = 1/16777216 = 5.96*(10^-8) kilogram
60 minutes = 1 hour.
The bateria at the end of the hour divides itself into 2. This implies the bacteria becomes double after each hour.
So at the end of one hour it becomes 2.
At the end of the 2nd hr it becomes 2^2.
At the end of the 3rd hour it becomes 2^3 and so on and at the end of the 24 hour the bacteria becomes 2^24 whose mass = 1Kg. So the mass of the single bacterium = 1KG/2^24 = 2^(-24) Kg = 1000 gram/2^24 = =5.960464478*10^(-5) gram.