Answer:
There will be 50 bacteria remaining after 28 minutes.
Step-by-step explanation:
The exponential decay equation is
![N=N_0e^{-rt}](https://tex.z-dn.net/?f=N%3DN_0e%5E%7B-rt%7D)
N= Number of bacteria after t minutes.
= 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
= 500
t=11 minutes
r=?
![N=N_0e^{-rt}](https://tex.z-dn.net/?f=N%3DN_0e%5E%7B-rt%7D)
![\therefore 200=500e^{-11r}](https://tex.z-dn.net/?f=%5Ctherefore%20200%3D500e%5E%7B-11r%7D)
![\Rightarrow e^{-11r}=\frac{200}{500}](https://tex.z-dn.net/?f=%5CRightarrow%20e%5E%7B-11r%7D%3D%5Cfrac%7B200%7D%7B500%7D)
Taking ln both sides
![\Rightarrow ln| e^{-11r}|=ln|\frac{2}{5}|](https://tex.z-dn.net/?f=%5CRightarrow%20ln%7C%20e%5E%7B-11r%7D%7C%3Dln%7C%5Cfrac%7B2%7D%7B5%7D%7C)
![\Rightarrow {-11r}=ln|\frac{2}{5}|](https://tex.z-dn.net/?f=%5CRightarrow%20%7B-11r%7D%3Dln%7C%5Cfrac%7B2%7D%7B5%7D%7C)
![\Rightarrow r}=\frac{ln|\frac{2}{5}|}{-11}](https://tex.z-dn.net/?f=%5CRightarrow%20r%7D%3D%5Cfrac%7Bln%7C%5Cfrac%7B2%7D%7B5%7D%7C%7D%7B-11%7D)
To find the time when there will be 50 bacteria remaining, we plug N=50,
= 500 and
in exponential decay equation.
![50=500e^{-\frac{ln|\frac25|}{-11}.t}](https://tex.z-dn.net/?f=50%3D500e%5E%7B-%5Cfrac%7Bln%7C%5Cfrac25%7C%7D%7B-11%7D.t%7D)
![\Rightarrow \frac{50}{500}=e^{\frac{ln|\frac25|}{11}.t}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B50%7D%7B500%7D%3De%5E%7B%5Cfrac%7Bln%7C%5Cfrac25%7C%7D%7B11%7D.t%7D)
Taking ln both sides
![\Rightarrow ln|\frac{50}{500}|=ln|e^{\frac{ln|\frac25|}{11}.t}|](https://tex.z-dn.net/?f=%5CRightarrow%20ln%7C%5Cfrac%7B50%7D%7B500%7D%7C%3Dln%7Ce%5E%7B%5Cfrac%7Bln%7C%5Cfrac25%7C%7D%7B11%7D.t%7D%7C)
![\Rightarrow ln|\frac{1}{10}|={\frac{ln|\frac25|}{11}.t}](https://tex.z-dn.net/?f=%5CRightarrow%20ln%7C%5Cfrac%7B1%7D%7B10%7D%7C%3D%7B%5Cfrac%7Bln%7C%5Cfrac25%7C%7D%7B11%7D.t%7D)
![\Rightarrow t= \frac{ln|\frac{1}{10}|}{\frac{ln|\frac25|}{11}.}](https://tex.z-dn.net/?f=%5CRightarrow%20t%3D%20%5Cfrac%7Bln%7C%5Cfrac%7B1%7D%7B10%7D%7C%7D%7B%5Cfrac%7Bln%7C%5Cfrac25%7C%7D%7B11%7D.%7D)
![\Rightarrow t= \frac{11\times ln|\frac{1}{10}|}{{ln|\frac25|}}](https://tex.z-dn.net/?f=%5CRightarrow%20t%3D%20%5Cfrac%7B11%5Ctimes%20ln%7C%5Cfrac%7B1%7D%7B10%7D%7C%7D%7B%7Bln%7C%5Cfrac25%7C%7D%7D)
minutes
There will be 50 bacteria remaining after 28 minutes.
Answer:
Arnie
Step-by-step explanation:
Arnie : 34 ÷ 16 = 2.2
Maria : 18÷ 15= 1.2
i think the answer is A
Step-by-step explanation:
i just think it's a