The function that represents the total profit of the two stores combined over time from 2000 to 2015 is Total profit(x)=−0.60x+21.63.
To find the function that represents the total profit of the two stores combined, you'll want to add the profits of the two stores at each corresponding point in time (represented by 'x').
The given functions represent the profits of the two branches over time:
f(x)=0.15x+6.53
g(x)=−0.75x+15.10
To find the total profit, you simply add the profits from both stores for any given 'x' value. So, the function representing the total profit would be the sum of these two functions:
Total profit(x)=f(x)+g(x)
Total profit(x)=(0.15x+6.53)+(−0.75x+15.10)
Combine like terms:
Total profit(x)=0.15x−0.75x+6.53+15.10
Total profit(x)=−0.60x+21.63
So, the function that represents the total profit of the two stores combined over time from 2000 to 2015 is:
Total profit(x)=−0.60x+21.63