A sample of bacteria is being eradicated by an experimental procedure. The population is following a pattern of exponential decay and approaching a population of 0. If the sampl…

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asked Jul 5, 2021 114k views

1 Answer

Deorst · Answer 1 · 2021-07-09T19:06:00+0000

Answer:

There will be 50 bacteria remaining after 28 minutes.

Explanation:

The exponential decay equation is

N=N_0e^(-rt)

N= Number of bacteria after t minutes.

N_0 = Initial number of bacteria when t=0.

r= Rate of decay per minute

t= time is in minute.

The sample begins with 500 bacteria and after 11 minutes there are 200 bacteria.

N=200

N_0 = 500

t=11 minutes

r=?

N=N_0e^(-rt)

$\therefore 200=500e^(-11r)$

$\Rightarrow e^(-11r)=(200)/(500)$

Taking ln both sides

$\Rightarrow ln| e^(-11r)|=ln|(2)/(5)|$

$\Rightarrow {-11r}=ln|(2)/(5)|$

$\Rightarrow r}=(ln|(2)/(5)|)/(-11)$

To find the time when there will be 50 bacteria remaining, we plug N=50,
N_0 = 500 and
r}=(ln|(2)/(5)|)/(-11) in exponential decay equation.

50=500e^)/(-11).t

$\Rightarrow (50)/(500)=e^\frac25$

Taking ln both sides

$\Rightarrow ln|(50)/(500)|=ln|e^\frac25|$

$\Rightarrow ln|(1)/(10)|=)/(11).t$

$\Rightarrow t= (ln|(1)/(10)|)/((ln|\frac25|)/(11).)$

$\Rightarrow t= \frac(1)/(10){ln}$

$\Rightarrow t\approx 28$ minutes

There will be 50 bacteria remaining after 28 minutes.