In a Biology experiment, you are charged with finding the average growth rate of

Question

In a Biology experiment, you are charged with finding the average growth rate of a bacteria colony. At 8:00 a.m. on day 1, you estimate the colony to be roughly circular with a radius of 1 cm and a depth of 2mm. Due to the irregularity of the colony, you estimate that the radius varies between 0.96 cm to 1.05 cm. The depth of the colony looks fairly uniform but it is rather difficult to probe the depth of the colony in the culture so you estimate that the uncertainity in the depth is about 0.3 mm. On the following day at 2:00 p.m., you measure the size of the colony again and using the same process, decide that the colony has grown to: Radius: 1.5 cm +/- 0.03 cm. Depth: 3.4 mm +/- 0.3 mm. (e) Calculate the uncertainty in the volume of the colony on day 1. (f) Calculate the uncertainty in the volume of the colony on day 2. (g) As the measurements on the two different days are independent, you can now calculate the uncertainty in the change in volume using the results in parts (e) and (f). This two step process does not work if the two volumes are not independent they depend on a common variable. (h) What would you report to your advisor as the uncertainty in your growth rate? (i) If your advisor is not happy with the accuracy of your results-i.e. she feels the error margin (uncertainty) is too large, which of your two measurements, radius and depth should you pay more attention to when you repeat the experiment? Justify your answer.

Explanation / Answer

e)

V = pi*r^2*d

Uncertainity in volume is deltaV

We have,

deltaV/V = deltad/d + 2deltar/r

deltaV/V = 0.3/2 + 2*0.045/1

delta V /V = 0.24

delta V = 0.24*V

delta V = 0.24*pi*10^-4*2*10^-3

delta V = 1.5 * 10^-7 m3

f)

Uncertainity in volume on day 2 is deltaV

We have,

deltaV/V = deltad/d + 2deltar/r

deltaV/V = 0.3/3.4 + 2*0.03/1.5

delta V /V = 0.128

delta V = 0.128*V

delta V = 0.128*1.5^2*3.4*pi*10^-4*10^-3

delta V = 3.074 * 10^-7 m3

g)

Uncertainity in Volume is (3.074+1.5)*10^-7/2

Uncertainity is 2.287*10^-7 m3

h)

Radius plays a key role as the incertainity in radius contributes double to the error margin in Volume

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