Answer:
The shape has 6 angles and 6 sides
Step-by-step explanation:
therefore it is a hexigon as hexigon is a polygon of six angles and six sides.
The area of a square or a rectangle (which is the shape of any room in a house) is:
Area = width x length
So, in this case:
Area = 51 m x 26 m = 1326 Sq meters. Which is pretty big if you ask me.
Anyhow, Ms Melcher needs to buy 1326 sq meters
To model this situation, we are going to use the exponential function:
![f(t)=P(1+ \frac{r}{n} )^{nt}](https://tex.z-dn.net/?f=f%28t%29%3DP%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D)
where
![P](https://tex.z-dn.net/?f=P)
is the initial number of cars
![r](https://tex.z-dn.net/?f=r)
is the growing rate in decimal form
![n](https://tex.z-dn.net/?f=n)
is number of tames the growing rate is increasing per year
![t](https://tex.z-dn.net/?f=t)
is the time in years
To convert the growing rate to decimal form, we are going to divide the rate by 100%
![r= \frac{12}{100}](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7B12%7D%7B100%7D%20)
![r=0.12](https://tex.z-dn.net/?f=r%3D0.12)
Since the growing rate is increasing quarterly,
![n=4](https://tex.z-dn.net/?f=n%3D4)
. We also know that the initial number of cars is 920, so
![P=920](https://tex.z-dn.net/?f=P%3D920)
. Lets replace all those values in our function:
![f(t)=920(1+ \frac{0.12}{4} )^{4t}](https://tex.z-dn.net/?f=f%28t%29%3D920%281%2B%20%5Cfrac%7B0.12%7D%7B4%7D%20%29%5E%7B4t%7D)
![f(t)=920(1+0.03)^{4t}](https://tex.z-dn.net/?f=f%28t%29%3D920%281%2B0.03%29%5E%7B4t%7D)
![f(t)=900(1.03)^{4t}](https://tex.z-dn.net/?f=f%28t%29%3D900%281.03%29%5E%7B4t%7D)
We can conclude that:
Rate ---------> The quarterly rate of growth is 0.03 or 3%
Exponent --------> The compound periods multiplied by the number of years is 4t
Coefficient--------> The initial number of cars serviced is 920
Base------> The growth factor is represented by 1.03