Answer :
Answer:
[tex]g(x) = 9.6\cdot x -40[/tex]; The team shall earn $ 632 for selling 70 candles.
Step-by-step explanation:
We notice that statement indicate that every worker gains 80 percent of the revenue for selling candles, which is represented [tex]f(x) = 12\cdot x[/tex], where [tex]x[/tex] is the quantity of sold candles and [tex]f(x)[/tex] is measured in US dollars, minus 40 US dollars. Then, the mathematical expression [tex]g(x)[/tex] is formed by three components:
1) Revenue for selling candles: [tex]f(x)[/tex]
2) 80 % of the revenue for selling candles: Vertical scaling ([tex]k = 0.8[/tex])
3) $ 40 are subtracted: Vertical translation. ([tex]b = -40[/tex])
Then, the expression for [tex]g(x)[/tex] is:
[tex]g(x) = k\cdot f(x) +b[/tex]
[tex]g(x) = 0.8\cdot (12\cdot x) -40[/tex]
[tex]g(x) = 9.6\cdot x -40[/tex]
Where:
[tex]x[/tex] - Quantity of candles, dimensionless.
[tex]g(x)[/tex] - Team's profit, measured in US dollars.
Finally, we determine the profit for selling 70 candles: ([tex]x = 70[/tex])
[tex]g(70) = 9.6\cdot (70) - 40[/tex]
[tex]g(70) = 632[/tex]
The team shall earn $ 632 for selling 70 candles.