Respuesta :
Answer:
A = 1013.25
Explanation:
First we will find the rate of decrease of population of bacteria
As we know that
[tex]A = A_0*e^{kt}[/tex]
Where A is the final population
[tex]A_0 =[/tex] the initial population
K is the rate of decrease of population
t is the time period
Substituting the given values, we get -
[tex]100 = 100,000 * e ^{k *24}\\[/tex]
[tex]10^{-3} = e^{k*24}[/tex]
taking antilog on both sides, we get -
- 6.907 = k *24
k = -0.287 /hr
Now,
After 16 hour the population would be
[tex]A = 100,000 * e*{-0.287*16}\\A = 1013.25[/tex]
In 16 hours 66,667 number of bacteria were eliminated from the population of 100,000 bacteria.
Researchers recorded that a certain bacteria population decrease from 100,000 to 100 in 24 hours which means that in every hour 4167 number of bacteria were killed or eliminated.
If for one hour, 4167 number of bacteria were killed then in after 16 hours 66,667 number of bacteria were killed or eliminated from the population of 100,000 bacteria so we can conclude that in 16 hours 66,667 number of bacteria were eliminated from the population of 100,000 bacteria.
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