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
Explanation:
Branch A:
First year profit = $50,000
The profit increased by 4% every year
Formula :

So, Total profit after x years =

=

Branch B:
First year profit = $35000
The profit increased by 5.5% every year
Formula :

So, Total profit after x years =

=

Thus the function of total profit of fast food chain :


Now to find total profit after four years .
Substitute x = 4
![P(4)=5000[10(1.04)^4+7(1.055)^4]](https://img.qammunity.org/2018/formulas/mathematics/college/pvin1dudqgmczt08j1h1vil9cn3bm8cxtp.png)

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