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1 vote
A culture started with 6,000 bacteria. After 4

hours, it grew to 7,800 bacteria. Predict how
many bacteria will be present after 18 hours.
Round your answer to the nearest whole
number.
P- Aekt

User SnowFatal
by
9.0k points

1 Answer

4 votes

19539 bacteria will be present after 18 hours

Solution:

Initial value of bacteria N = 6000

Value after 4 hours
N_o = 7800

The standard exponential equation is given as:


N=N_(o) E^(-k t)

where

N is amount after time t

No is the initial amount

k is the constant rate of growth

t is time

Plugging in the values in formula we get,


7800 = 6000E^(-4k)

Solving for "k" we get,


(13)/(10)=E^(-4k)

Taking "ln" on both sides, we get


ln(13)/(10) = -4k


(ln(13)/(10))/(4) = -k

On solving for ln, we get k = -0.0656

The equation becomes,
N = 6000E^(0.0656t)

Now put "t" = 18,


N = 6000E^(0.0656 * 18)\\\\N = 6000 * 3.256 = 19539

Hence the bacteria present after 18 hours is 19539

User Billjk
by
7.4k points
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