Answer:
The function can the fast food chain use to determine its total profit, P(x), after x years :
Total profit after 4 years = $101,851.79
Step-by-step explanation:
Branch A:
First year profit = $50,000
The profit increased by 4% every year
Formula : ![A =P(1+r)^t](https://tex.z-dn.net/?f=A%20%3DP%281%2Br%29%5Et)
So, Total profit after x years = ![P(x)=50,000(1+0.04)^x](https://tex.z-dn.net/?f=P%28x%29%3D50%2C000%281%2B0.04%29%5Ex)
= ![P(x)=50,000(1.04)^x](https://tex.z-dn.net/?f=P%28x%29%3D50%2C000%281.04%29%5Ex)
Branch B:
First year profit = $35000
The profit increased by 5.5% every year
Formula : ![A =P(1+r)^t](https://tex.z-dn.net/?f=A%20%3DP%281%2Br%29%5Et)
So, Total profit after x years = ![P(x)=35,000(1+0.055)^x](https://tex.z-dn.net/?f=P%28x%29%3D35%2C000%281%2B0.055%29%5Ex)
= ![P(x)=35,000(1.055)^x](https://tex.z-dn.net/?f=P%28x%29%3D35%2C000%281.055%29%5Ex)
Thus the function of total profit of fast food chain :
![P(x)=50,000(1.04)^x+35,000(1.055)^x](https://tex.z-dn.net/?f=P%28x%29%3D50%2C000%281.04%29%5Ex%2B35%2C000%281.055%29%5Ex)
![P(x)=5000[10(1.04)^x+7(1.055)^x](https://tex.z-dn.net/?f=P%28x%29%3D5000%5B10%281.04%29%5Ex%2B7%281.055%29%5Ex)
Now to find total profit after four years .
Substitute x = 4
![P(4)=5000[10(1.04)^4+7(1.055)^4]](https://tex.z-dn.net/?f=P%284%29%3D5000%5B10%281.04%29%5E4%2B7%281.055%29%5E4%5D)
![P(4)=101851.790772](https://tex.z-dn.net/?f=P%284%29%3D101851.790772)
Hence Option D is correct.
The function can the fast food chain use to determine its total profit, P(x), after x years :
Total profit after 4 years = $101,851.79