Answer:
The number of bacteria after t hours is given by: ![y(t) = 100e^{0.3219t}](https://tex.z-dn.net/?f=y%28t%29%20%3D%20100e%5E%7B0.3219t%7D)
Step-by-step explanation:
Amount of bacteria after t hours:
Is given by the following equation:
![y(t) = ae^{kt}](https://tex.z-dn.net/?f=y%28t%29%20%3D%20ae%5E%7Bkt%7D)
In which a is the initial value and k is the constant of growth.
There are 100 bacteria initially
This means that
. So
![y(t) = ae^{kt}](https://tex.z-dn.net/?f=y%28t%29%20%3D%20ae%5E%7Bkt%7D)
![y(t) = 100e^{kt}](https://tex.z-dn.net/?f=y%28t%29%20%3D%20100e%5E%7Bkt%7D)
500 bacteria five hours later.
This means that
. We use this to find k. So
![y(t) = 100e^{kt}](https://tex.z-dn.net/?f=y%28t%29%20%3D%20100e%5E%7Bkt%7D)
![500 = 100e^{5k}](https://tex.z-dn.net/?f=500%20%3D%20100e%5E%7B5k%7D)
![e^{5k} = 5](https://tex.z-dn.net/?f=e%5E%7B5k%7D%20%3D%205)
![\ln{e^{5k}} = \ln{5}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B5k%7D%7D%20%3D%20%5Cln%7B5%7D)
![5k = \ln{5}](https://tex.z-dn.net/?f=5k%20%3D%20%5Cln%7B5%7D)
![k = \frac{\ln{5}}{5}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B%5Cln%7B5%7D%7D%7B5%7D)
![k = 0.3219](https://tex.z-dn.net/?f=k%20%3D%200.3219)
So
![y(t) = 100e^{kt}](https://tex.z-dn.net/?f=y%28t%29%20%3D%20100e%5E%7Bkt%7D)
![y(t) = 100e^{0.3219t}](https://tex.z-dn.net/?f=y%28t%29%20%3D%20100e%5E%7B0.3219t%7D)
The number of bacteria after t hours is given by: ![y(t) = 100e^{0.3219t}](https://tex.z-dn.net/?f=y%28t%29%20%3D%20100e%5E%7B0.3219t%7D)
Answer:
SAS
Step-by-step explanation:
The sides have the same ratio and the angle between them is congruent, so it's SAS
Answer:
A&C
Step-by-step explanation:
Answer:
Step-by-step explanation:
<u>Use the formula:</u>
- A = 1/2Pa, where P- perimeter, a - apothem
<u>Find the area:</u>
- A = 1/2(5*17.6)*12.1 = 532.4 in²
Correct choice is d
Answer:
![~Hi,~There!](https://tex.z-dn.net/?f=~Hi%2C~There%21)
How would 5,708,942,013 be written in word form?
A. five million, seven hundred eight thousand, nine hundred forty-two thousand, thirteen
Hope this helps!