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21 Jul 2022, 14:04
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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61% (02:35) correct
39%
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wrong
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In a certain population of microbes in a petri dish, the rate of increase in the population is 9 percent per hour. The time it takes for a given population to double can be estimated using the formula \(\frac{70}{t}\) hours, where t is the rate of increase per hour expressed as a percent. If the number of microbes in the dish is 60,000 at the start of the first hour, what will be the approximate number of microbes after 48 hours?
A) 120,000
B) 420,000
C) 720,000
D) 1,900,000
E) 3,800,000
A) 120,000
B) 420,000
C) 720,000
D) 1,900,000
E) 3,800,000
21 Jul 2022, 15:38
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After 70/9 = 7 + 7/9 hours the population doubles
48hrs corresponds to (a little bit more than) six times the above span of time:
6 * (7 + 7/9) = 42 + 42/9 = 46 + 2/3
2 ^ 6 = 64
Best estimate for the final population = 60.000 * 64 = 3.840.000,00
Correct answer: E
Just one question for the master users...:
Precise final number of microbes: 60.000 * 1,09 ^ 48 = 3.755.114,22
While according to the given estimating formula, the result would be: 2 ^ (48/70*9) * 60.000 = 4.324.504,63
Why is the estimate so distant from the real result? Am I missing something or is the estimate provided by the text of the problem just as a simple aid to get to the solution and doesn't necessarily have to be extremely accurate? Differently, how was it calculated/can be calculated such an estimate?
Am I missing something?
Thanks
Posted from my mobile device
48hrs corresponds to (a little bit more than) six times the above span of time:
6 * (7 + 7/9) = 42 + 42/9 = 46 + 2/3
2 ^ 6 = 64
Best estimate for the final population = 60.000 * 64 = 3.840.000,00
Correct answer: E
Just one question for the master users...:
Precise final number of microbes: 60.000 * 1,09 ^ 48 = 3.755.114,22
While according to the given estimating formula, the result would be: 2 ^ (48/70*9) * 60.000 = 4.324.504,63
Why is the estimate so distant from the real result? Am I missing something or is the estimate provided by the text of the problem just as a simple aid to get to the solution and doesn't necessarily have to be extremely accurate? Differently, how was it calculated/can be calculated such an estimate?
Am I missing something?
Thanks
Posted from my mobile device
29 Jan 2025, 23:37
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