Answer:
28 is the LCM (least common multiple)
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Answer:
9,942 bacteria were there at 10 hours.
Step-by-step explanation:
Equation for population decay:
The equation for population decay, after t hours, is given by:
![P(t) = P(0)(1-r)^t](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281-r%29%5Et)
In which P(0) is the initial population and r is the decay rate, as a decimal.
Researchers recorded that a certain bacteria population declined from 200,000 to 900 in 18 hours.
This means that
and that when
. So we use this to find r.
![P(t) = P(0)(1-r)^t](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281-r%29%5Et)
![900 = 200000(1-r)^{18}](https://tex.z-dn.net/?f=900%20%3D%20200000%281-r%29%5E%7B18%7D)
![(1-r)^{18} = \frac{900}{200000}](https://tex.z-dn.net/?f=%281-r%29%5E%7B18%7D%20%3D%20%5Cfrac%7B900%7D%7B200000%7D)
![\sqrt[18]{(1-r)^{18}} = \sqrt[18]{\frac{900}{200000}}](https://tex.z-dn.net/?f=%5Csqrt%5B18%5D%7B%281-r%29%5E%7B18%7D%7D%20%3D%20%5Csqrt%5B18%5D%7B%5Cfrac%7B900%7D%7B200000%7D%7D)
![1 - r = (\frac{900}{200000})^{\frac{1}{18}}](https://tex.z-dn.net/?f=1%20-%20r%20%3D%20%28%5Cfrac%7B900%7D%7B200000%7D%29%5E%7B%5Cfrac%7B1%7D%7B18%7D%7D)
![1 - r = 0.7407](https://tex.z-dn.net/?f=1%20-%20r%20%3D%200.7407)
So
![P(t) = P(0)(1-r)^t](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281-r%29%5Et)
![P(t) = 200000(0.7407)^t](https://tex.z-dn.net/?f=P%28t%29%20%3D%20200000%280.7407%29%5Et)
At this rate of decay, how many bacteria was there at 10 hours?
This is P(10). So
![P(10) = 200000(0.7407)^{10} = 9941.5](https://tex.z-dn.net/?f=P%2810%29%20%3D%20200000%280.7407%29%5E%7B10%7D%20%3D%209941.5)
Rounding to the nearest whole number:
9,942 bacteria were there at 10 hours.
Answer:
You fill it up to be 8/8 Full
Step-by-step explanation:
Theres not enough information to answer this for you,