MATH SOLVE

3 months ago

Q:
# HEEEEEEEEEEEEEEEEELLPPPPPPPPPPA famous fast food chain opened two branches in different parts of a city. Branch A made a profit of $50,000 in the first year, and the profit increased by 4% every year. Branch B made a profit of $35,000 in the first year, and the profit increased by 5.5% every year.Which function can the fast food chain use to determine its total profit, P(x), after x years, and how much money will the chain have made in profit after 4 years?A)P(x) = 5,000(10(1.055)x + 7(1.04)x); $97,341.65B)P(x) = 5,000(10(1.04)x + 7(1.055)x); $73,017.93C)P(x) = 5,000(10(1.055)x + 7(1.04)x); $106,576.25D)P(x) = 5,000(10(1.04)x + 7(1.055)x); $101,851.79

Accepted Solution

A:

Answer:The function can the fast food chain use to determine its total profit, P(x), after x years : [tex]P(x)=5000[10(1.04)^x+7(1.055)^x[/tex] Total profit after 4 years = $101,851.79Step-by-step explanation:Branch A:First year profit = $50,000The profit increased by 4% every yearFormula : [tex]A =P(1+r)^t[/tex]So, Total profit after x years = [tex]P(x)=50,000(1+0.04)^x[/tex] = [tex]P(x)=50,000(1.04)^x[/tex]Branch B:First year profit = $35000The profit increased by 5.5% every yearFormula : [tex]A =P(1+r)^t[/tex]So, Total profit after x years = [tex]P(x)=35,000(1+0.055)^x[/tex] = [tex]P(x)=35,000(1.055)^x[/tex]Thus the function of total profit of fast food chain :[tex]P(x)=50,000(1.04)^x+35,000(1.055)^x[/tex][tex]P(x)=5000[10(1.04)^x+7(1.055)^x[/tex]Now to find total profit after four years .Substitute x = 4[tex]P(4)=5000[10(1.04)^4+7(1.055)^4][/tex][tex]P(4)=101851.790772[/tex]Hence Option D is correct.The function can the fast food chain use to determine its total profit, P(x), after x years : [tex]P(x)=5000[10(1.04)^x+7(1.055)^x[/tex] Total profit after 4 years = $101,851.79