The degree of an individual term of a polynomial is the exponent of its variable; the exponents of the terms of this polynomial are, in order, 5, 4, 2, and 7. The degree of the polynomial is the highest degree of any of the terms; in this case, it is 7.
Answer:
1.![\frac{dy}{dt}=ky](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%3Dky)
2.543.6
Step-by-step explanation:
We are given that
y(0)=200
Let y be the number of bacteria at any time
=Number of bacteria per unit time
![\frac{dy}{dt}\proportional y](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%5Cproportional%20y)
![\frac{dy}{dt}=ky](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%3Dky)
Where k=Proportionality constant
2.
,y'(0)=100
Integrating on both sides then, we get
![lny=kt+C](https://tex.z-dn.net/?f=lny%3Dkt%2BC)
We have y(0)=200
Substitute the values then , we get
![ln 200=k(0)+C](https://tex.z-dn.net/?f=ln%20200%3Dk%280%29%2BC)
![C=ln 200](https://tex.z-dn.net/?f=C%3Dln%20200)
Substitute the value of C then we get
![ln y=kt+ln 200](https://tex.z-dn.net/?f=ln%20y%3Dkt%2Bln%20200)
![ln y-ln200=kt](https://tex.z-dn.net/?f=ln%20y-ln200%3Dkt)
![ln\frac{y}{200}=kt](https://tex.z-dn.net/?f=ln%5Cfrac%7By%7D%7B200%7D%3Dkt)
![\frac{y}{200}=e^{kt}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B200%7D%3De%5E%7Bkt%7D)
![y=200e^{kt}](https://tex.z-dn.net/?f=y%3D200e%5E%7Bkt%7D)
Differentiate w.r.t
![y'=200ke^{kt}](https://tex.z-dn.net/?f=y%27%3D200ke%5E%7Bkt%7D)
Substitute the given condition then, we get
![100=200ke^{0}=200 \;because \;e^0=1](https://tex.z-dn.net/?f=100%3D200ke%5E%7B0%7D%3D200%20%5C%3Bbecause%20%5C%3Be%5E0%3D1)
![k=\frac{100}{200}=\frac{1}{2}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B100%7D%7B200%7D%3D%5Cfrac%7B1%7D%7B2%7D)
![y=200e^{\frac{t}{2}}](https://tex.z-dn.net/?f=y%3D200e%5E%7B%5Cfrac%7Bt%7D%7B2%7D%7D)
Substitute t=2
Then, we get ![y=200e^{\frac{2}{2}}=200e](https://tex.z-dn.net/?f=y%3D200e%5E%7B%5Cfrac%7B2%7D%7B2%7D%7D%3D200e)
![y=200(2.718)=543.6=543.6](https://tex.z-dn.net/?f=y%3D200%282.718%29%3D543.6%3D543.6)
e=2.718
Hence, the number of bacteria after 2 hours=543.6
Do you mean as a decimal? 11.8
Answer:
c
Step-by-step explanation:
1=x
-3=y
then you plug it in. put the -3 in for the y and the 1 in for the x then you have the equation:
-3<3(1)+1
and solve it
-3<4+1
-3<5
Answer: The answer is 0.8 liters of water.
Step-by-step explanation: Well there are 5 cats and each cat drinks .15 liters per day. .15x5 = .75 liters of water. 1.55 liters - .75 liters = 0.8 liters left.