Researchers recorded that a certain bacteria population declined from 170,000 to 200 in 42 hours. At this rate of decay, how many bacteria was there at 24 hours? Round to the nearest whole number.

Question

Mathematics

Aimee Webster

19 March, 05:29

Researchers recorded that a certain bacteria population declined from 170,000 to 200 in 42 hours. At this rate of decay, how many bacteria was there at 24 hours? Round to the nearest whole number.

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Janae Moore · Answer 1

3600 bacterias

Step-by-step explanation:

From P = P'e^ (-kt), where

P = final population

P' = initial population

k = decay constant

t = time in hrs

Substituting we have

200 = 170000 x e^ (-42k)

1/850 = e^ (-42k)

We take natural log (Ln) of both side

Ln (1/850) = Ln (e^ (-42k))

-6.745 = - 42k

k = 0.16059.

For amount remaining after 24 hrs we find P

P = 170000 x e^ (-0.16059x24)

P = 170000 x e^-3.85416

P = 170000 x 0.02119 = 3602.3

Approximately 3600 bacterias.