Answer:
![P(t) = 100e^{0.0251t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20100e%5E%7B0.0251t%7D)
The doubling time is of 27.65 minutes.
Step-by-step explanation:
Exponential equation of growth:
The exponential equation for population growth is given by:
![P(t) = P(0)e^{kt}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29e%5E%7Bkt%7D)
In which P(0) is the initial value and k is the growth rate.
A freshly inoculated bacterial culture of Streptococcus contains 100 cells.
This means that
. So
![P(t) = 100e^{kt}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20100e%5E%7Bkt%7D)
When the culture is checked 60 minutes later, it is determined that there are 450 cells present.
This means that
, and we use this to find k. So
![450 = 100e^{60k}](https://tex.z-dn.net/?f=450%20%3D%20100e%5E%7B60k%7D)
![e^{60k} = 4.5](https://tex.z-dn.net/?f=e%5E%7B60k%7D%20%3D%204.5)
![\ln{e^{60k}} = \ln{4.5}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B60k%7D%7D%20%3D%20%5Cln%7B4.5%7D)
![60k = \ln{4.5}](https://tex.z-dn.net/?f=60k%20%3D%20%5Cln%7B4.5%7D)
![k = \frac{\ln{4.5}}{60}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B%5Cln%7B4.5%7D%7D%7B60%7D)
![k = 0.0251](https://tex.z-dn.net/?f=k%20%3D%200.0251)
So
![P(t) = 100e^{0.0251t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20100e%5E%7B0.0251t%7D)
Doubling time:
This is t for which P(t) = 2P(0) = 200. So
![200 = 100e^{0.0251t}](https://tex.z-dn.net/?f=200%20%3D%20100e%5E%7B0.0251t%7D)
![e^{0.0251t} = 2](https://tex.z-dn.net/?f=e%5E%7B0.0251t%7D%20%3D%202)
![\ln{e^{0.0251t}} = \ln{2}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B0.0251t%7D%7D%20%3D%20%5Cln%7B2%7D)
![0.0251t = \ln{2}](https://tex.z-dn.net/?f=0.0251t%20%3D%20%5Cln%7B2%7D)
![t = \frac{\ln{2}}{0.0251}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Cln%7B2%7D%7D%7B0.0251%7D)
![t = 27.65](https://tex.z-dn.net/?f=t%20%3D%2027.65)
The doubling time is of 27.65 minutes.
2b because you would have to multiply which b means 1 so it will be 2b.
Answer:
6.7-(-2.5)=9.2 6.7+(-2.5)=4.2 Neither
2.5 + 6.7 6.7 - 2.5 2.5 - 6.7
-2.5 + 6.7 -2.5 - 6.7
-6.7 + 2.5
Answer:
B. $8
Step-by-step explanation:
Given:
Total payment, T = $160
Hourly rates = $t/hour
= total payment/total time worked
The question said, "worked 12 more hours than the amount she is paid per hour".
Total time worked = (12 + t) hour
Therefore, Hourly rates of payment, t = 160/(12 + t)
t^2 + 12t - 160 = 0
Solving the above quadratic equation,
t = -20 and 8
t = $8
Answer:
Step-by-step explanation
Use Pythagoras theorem. The distance between the cars, 8km, is the hypotenuse of a right angled triangle, one leg of which is 6km and the other of which is, say, x km
x = sqrt(8^2 - 6^2) km.
You can crunch the numbers.