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:
300G
Step-by-step explanation:
Here is the complete question
A wedding cake weighed 8kg. If 2/5th of its weight was flour, 5/16th was sugar,1/4th was cream and the rest were nuts, find the weight of nuts.
fraction of the cake that was nuts = 1 - (2/5 + 5/16 + 1/4)
1 -
= 3/80
wight of nuts = 3/80 x 8 = 0.3 kg = 300g
2/7 srry if I'm wrong because they are parellel and possibly the same