Researchers recorded that a certain bacteria population declined from 100,000 to 100 in 24 hours. At this rate of decay, how many bacteria were there 8 hours into the experiment?

9990bacterias

Step-by-step explanation:

Using the formula for finding rate of decay.

N(t) = Noe^-kt

No is the initial population

N(t) is the population during time ,t

If bacteria population declined from 100,000 to 100 in 24 hours

No = 100,000, N(t) = 100, t = 24

Substituting to get the constant k

100 = 100000e^-24k

0.001 = e^-24k

Taking ln of both sides

ln0.001 = lne^-24k

-6.91 = -24k

k = 6.91/24

k = 0.288.

To know the number of bacteria there after 8hours,

N(8) = 100,000e^-0.288(8)

N(8) = 100,000e^-2.304

N(8) = 100,000×0.0999

N(8) = 9,990bacterias