Question

Research scientists need a certain type of bacteria to conduct an experiment. There are 2,500 bacteria in a certain culture. The culture grows at a rate of 25% daily. The scientists needs at least 10,000 bacteria to conduct an experiment. What is the least number of days they need to wait for the bacteria culture to reach a quantity of 10,000? (Hint: use a guess-and-check method to determine the lowest number of days that satisfy the requirement.)

Answer 1

Answer:

  7 days

Step-by-step explanation:

At 25% per day, it will take approximately 3 days to double the population, so approximately 6 days for the population to quadruple. Checking that number, we find it is not quite enough for the experiment, so another day is required.

"Guess and check" as a method of solution works especially well if you have an automated checker to evaluate your guess. A graphing calculator or spreadsheet can work well for this.

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We guess 3 days as the doubling time using the "rule of 72" that says the product of percentage and doubling time is about 72. That is, 72/25 ≈ 3. (This is only a very rough approximation of doubling time, best for rates near 8%.)