A 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?

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Аноним Аноним · Answer 1 · 2019-05-16T19:54:50+02:00

Oops wrong one man I’m sorry

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slicergiza slicergiza · Answer 2 · 2019-07-04T12:16:13+02:00

Answer: The function would be,

[tex]P(x)=50000(1.04)^x+35000(1.055)^x[/tex]

The approximate total profit after 4 years is $ 97341.65.

Step-by-step explanation:

Given,

For branch A,

First year profit = $ 50,000,

And, the profit increased by 4% every year.

Thus, the profit of branch A after x years,

[tex]P_1=50000(1+\frac{4}{100})^x[/tex]

[tex]\implies P_1=50000(1.04)^x[/tex]

Also, for branch B,

First year profit = $ 35,000,

And, the profit increased by 5.5% every year.

Thus, the profit of branch B after x years,

[tex]P_2=35000(1+\frac{5.5}{100})^x[/tex]

[tex]\implies P_2=35000(1.055)^x[/tex]

Hence, the total profit,

[tex]P=P_1+P_2[/tex]

[tex]\implies P(x)=50000(1.04)^x+35000(1.055)^x[/tex]

Which is the required function.

After 4 years, x = 3,

Therefore, the total profit after 4 years would be,

[tex]\implies P(3)=50000(1.04)^3+35000(1.055)^3=\$ 97341.648125\approx \$ 97341.65[/tex]