If
and
, separate variables in the differential equation to get
![e^{-y} \, dy = \sin(x) \, dx](https://tex.z-dn.net/?f=e%5E%7B-y%7D%20%5C%2C%20dy%20%3D%20%5Csin%28x%29%20%5C%2C%20dx)
Integrate both sides:
![\displaystyle \int e^{-y} \, dy = \int \sin(x) \, dx \implies -e^{-y} = -\cos(x) + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20e%5E%7B-y%7D%20%5C%2C%20dy%20%3D%20%5Cint%20%5Csin%28x%29%20%5C%2C%20dx%20%5Cimplies%20-e%5E%7B-y%7D%20%3D%20-%5Ccos%28x%29%20%2B%20C)
Use the initial condition to solve for
:
![-e^{-0} = -\cos(-\pi) + C \implies -1 = 1 + C \implies C = -2](https://tex.z-dn.net/?f=-e%5E%7B-0%7D%20%3D%20-%5Ccos%28-%5Cpi%29%20%2B%20C%20%5Cimplies%20-1%20%3D%201%20%2B%20C%20%5Cimplies%20C%20%3D%20-2)
Then the particular solution to the initial value problem is
![-e^{-y} = -\cos(x) - 2 \implies e^{-y} = \cos(x) + 2](https://tex.z-dn.net/?f=-e%5E%7B-y%7D%20%3D%20-%5Ccos%28x%29%20-%202%20%5Cimplies%20e%5E%7B-y%7D%20%3D%20%5Ccos%28x%29%20%2B%202)
(A)
Answer:
38,400 bacteria
Step-by-step explanation:
Because there are 24 hours in a day, it will double 4 times
2400times 2 equals 4800 (1st)
4800 times 2 equals 9600 (2nd)
9600 times 2 equals 19200 (3rd)
19200 times 2 equals 38400 (4th)
To work out the decrease, do original amount - new amount and then take that answer and divide it by the original amount, and then multiply by 100.
So you would do:
36.24 - 30.80 = 5.44
5.44 ÷ 36.24 × 100 = 15% to the nearest percent.