Dilution Series and Colony Counts
A lab technician serially dilutes a bacterial culture to estimate concentration. She performs three 1:10 dilutions in sequence, then plates 0.1 mL of the final dilution onto an agar plate. After incubation, she counts 42 colonies. A second plate, made from 0.1 mL of the second dilution, shows 4,180 colonies. The lab's countable range is 30–300 colonies per plate. A classmate suggests averaging the two counts to get a more reliable estimate.
1. Calculate the original culture concentration (CFU/mL) from each plate and decide which estimate should be reported.
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Final-dilution plate: total dilution = 10⁻³. Plated volume 0.1 mL = 10⁻¹ mL. CFU/mL = 42 ÷ (10⁻³ × 10⁻¹) = 42 ÷ 10⁻⁴ = 4.2 × 10⁵ CFU/mL.
Second-dilution plate: dilution = 10⁻². CFU/mL = 4,180 ÷ (10⁻² × 10⁻¹) = 4,180 ÷ 10⁻³ = 4.18 × 10⁶ CFU/mL.
Report the final-dilution estimate (4.2 × 10⁵ CFU/mL). Its 42 colonies fall inside the 30–300 countable range; 4,180 is far outside it (crowded plates undercount due to overlapping colonies).
2. Evaluate the classmate's suggestion to average the two estimates.
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Reject it. The two numbers differ by a factor of ~10, which signals the second plate is unreliable, not that averaging improves precision. Averaging a valid count with an out-of-range count produces a number that matches neither the method nor the data. The out-of-range plate should be discarded, not blended in.
3. The two estimates disagree by roughly 10-fold. Give the most likely procedural explanation and one check that would confirm it.
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Most likely explanation: a dilution step was miscounted or mislabeled - e.g., the "second dilution" plate was actually plated from the first dilution (10⁻¹), which would raise the calculated concentration by 10×. Check: recount the dilution tubes actually used, or re-plate from each tube to verify the series matches the labels before trusting either number.