Answer:
![y=2^{1-x}](https://tex.z-dn.net/?f=y%3D2%5E%7B1-x%7D)
Step-by-step explanation:
<u>Exponential Function</u>
When we need to express the exponential relation between two variables, we use the equation
![y=Cr^{x}](https://tex.z-dn.net/?f=y%3DCr%5E%7Bx%7D)
where C, r are constants to be determined by using the given points from the table
For x=0, y=2, thus
![2=C.r^{0}=C](https://tex.z-dn.net/?f=2%3DC.r%5E%7B0%7D%3DC)
We find that C=2
The equation is now
![y=2r^{x}](https://tex.z-dn.net/?f=y%3D2r%5E%7Bx%7D)
Now we use the point x=1, y=1
![1=2r](https://tex.z-dn.net/?f=1%3D2r)
We find that
![\displaystyle r=\frac{1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20r%3D%5Cfrac%7B1%7D%7B2%7D)
Thus, the equation is
![\displaystyle y=2\left(\frac{1}{2}\right)^{x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D2%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E%7Bx%7D)
Rearranging
![y=2(2)^{-x}=2^{1-x}](https://tex.z-dn.net/?f=y%3D2%282%29%5E%7B-x%7D%3D2%5E%7B1-x%7D)
The required equation is
![y=2^{1-x}](https://tex.z-dn.net/?f=y%3D2%5E%7B1-x%7D)
We can easily verify the last two points are also obtained by using the equation
For this case, the first thing we are going to do is define variables.
We have then:
x: number of birthday party goozy bags
y: total weight
We then have the following equation:
y = 150x + 200
For y = 6200 we have:
6200 = 150x + 200
Clearing x:
x = (6200-200) / (150)
x = 40
Answer:
there are 40 goody bags inside the box
Answer:
46
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
all go into 12