the population of a bacteria culture doubles every 2 minutes. approximately how many minutes will it take for the population to grow from 1,000 to 250,000+ bacteria?
Answers
Given : number of bacteria doubles over 2 minutes.
To Find : how long will it take for the population to grow from 1000 to 250000 +
Solution:
Initial a =1000
After 2* 1 = 2 minutes = 2 * 1000 = 2000 = 2¹ * 1000
After 2*2 = 4 minutes = 2 * 2000 = 4000 = 2² * 1000
After 2*3 = 6 minutes = 2 * 4000 = 8000 = 2³ * 1000
After 2*n = 2n minutes = 2ⁿ * 1000
2ⁿ * 1000 > 250000
=> 2ⁿ > 250
256 > 250
256 = 2⁸
=> 2⁸ > 250
=> n = 8
2 * 8 = 16 minutes
It will take 16 minutes for the population to grow from 1000 to 250000+
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The population of a bacteria culture doubles every 2 minutes.
» min 0 - 1,000
» min 2 - 2,000 = 1,000*2¹
» min 4 - 4000 = 1000*2²
» min 6 - 8000 = 1000*2³
So,
1000 * 2^x = 250,000
2^x = 250.
It asks you to approx. You know that 2⁸ = 256, so x = 8
★ Because the population doubles every 2 minutes, thus, time = 8*2 = 16 minutes.