To model this situation, we are going to use the standard linear function:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
.
1. Since S represent the total amount of money in the savings account,
![y=S](https://tex.z-dn.net/?f=y%3DS)
. We also know that each week she adds $40 to her account, so the slope of our linear equation will be
![40W](https://tex.z-dn.net/?f=40W)
; therefore,
![m=40W](https://tex.z-dn.net/?f=m%3D40W)
. Since she started her account with $750,
![b=750](https://tex.z-dn.net/?f=b%3D750)
.
Lets replace those values in our linear function:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
We can conclude that equation that models this situation is:
2. Now to find the total amount after 16 weeks, we just need to replace
![W](https://tex.z-dn.net/?f=W)
with 16 in our equation and simplify:
![S=40(16)+750](https://tex.z-dn.net/?f=S%3D40%2816%29%2B750)
![S=640+750](https://tex.z-dn.net/?f=S%3D640%2B750)
We can conclude that the amount of money in her account after 16 weeks is $1390
Answer:
; minimum
Step-by-step explanation:
Given:
The function is, ![y=x^{2}+2](https://tex.z-dn.net/?f=y%3Dx%5E%7B2%7D%2B2)
The given function represent a parabola and can be expressed in vertex form as:
![y=(x-0)^{2}+2](https://tex.z-dn.net/?f=y%3D%28x-0%29%5E%7B2%7D%2B2)
The vertex form of a parabola is
, where,
is the vertex.
So, the vertex is
.
In order to graph the given parabola, we find some points on it.
Let ![x=-2,y=(-2)^{2}+2=4+2=6](https://tex.z-dn.net/?f=x%3D-2%2Cy%3D%28-2%29%5E%7B2%7D%2B2%3D4%2B2%3D6)
![x=-1,y=(-1)^{2}+2=1+2=3](https://tex.z-dn.net/?f=x%3D-1%2Cy%3D%28-1%29%5E%7B2%7D%2B2%3D1%2B2%3D3)
![x=0,y=(0)^{2}+2=0+2=2](https://tex.z-dn.net/?f=x%3D0%2Cy%3D%280%29%5E%7B2%7D%2B2%3D0%2B2%3D2)
![x=2,y=(2)^{2}+2=4+2=6](https://tex.z-dn.net/?f=x%3D2%2Cy%3D%282%29%5E%7B2%7D%2B2%3D4%2B2%3D6)
![x=1,y=(1)^{2}+2=1+2=3](https://tex.z-dn.net/?f=x%3D1%2Cy%3D%281%29%5E%7B2%7D%2B2%3D1%2B2%3D3)
So, the points are
.
Mark these points on the graph and join them using a smooth curve.
The graph is shown below.
From the graph, we conclude that at the vertex
, it is minimum.