Question

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

Answer 1

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