Question

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?

Answer 1

Oops wrong one man I’m sorry

Answer 2

Answer: The function would be,

`P(x)=50000(1.04)^x+35000(1.055)^x`

The approximate total profit after 4 years is $ 97341.65.

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,

`P_1=50000(1+(4)/(100))^x`

`\implies P_1=50000(1.04)^x`

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,

`P_2=35000(1+(5.5)/(100))^x`

`\implies P_2=35000(1.055)^x`

Hence, the total profit,

`P=P_1+P_2`

`\implies P(x)=50000(1.04)^x+35000(1.055)^x`

Which is the required function.

After 4 years, x = 3,

Therefore, the total profit after 4 years would be,

`\implies P(3)=50000(1.04)^3+35000(1.055)^3=\$ 97341.648125\approx \$ 97341.65`