576 I hope this help cause I did this two years ago so I'm a little rusty but I think this is correct
do u need all the answers?
Answer:
y(x) = -2x -8
Step-by-step explanation:
using the hint, insert the points (x,y) in the equation:
-2 = -3m + b eq1
2 = -5m + b eq2
eq2 - eq1 :
4 = -2m ==> m = -2
insert m in eq1:
-2 = -3*(-2) +b ==> b = -8
Answer:
The graph is shown below.
The time to make the taste to half is <u>4.265 s.</u>
Step-by-step explanation:
Given:
Initial value of the taste is, ![Q_0=1](https://tex.z-dn.net/?f=Q_0%3D1)
Therefore, the quality of taste over time 't' is given as:
![Q(t)=Q_0(0.85)^t\\Q(t)=1(0.85)^t](https://tex.z-dn.net/?f=Q%28t%29%3DQ_0%280.85%29%5Et%5C%5CQ%28t%29%3D1%280.85%29%5Et)
Now, when the taste reduces to half, ![Q=0.5](https://tex.z-dn.net/?f=Q%3D0.5)
Therefore,
![0.5=1(0.85)^t](https://tex.z-dn.net/?f=0.5%3D1%280.85%29%5Et)
Taking natural log on both the sides, we get:
![\ln(0.5)=\ln(0.85)^t\\\ln(0.5)=t\ln(0.85)\\t=\frac{ln(0.5)}{\ln(0.85)}=4.265\ s](https://tex.z-dn.net/?f=%5Cln%280.5%29%3D%5Cln%280.85%29%5Et%5C%5C%5Cln%280.5%29%3Dt%5Cln%280.85%29%5C%5Ct%3D%5Cfrac%7Bln%280.5%29%7D%7B%5Cln%280.85%29%7D%3D4.265%5C%20s)
Therefore, the time to make the taste to half is <u>4.265 s.</u>