Respuesta :
Solution:
Given:
[tex]P(n)=415n-10790[/tex]This is a linear function.
The general form of a linear function is;
[tex]\begin{gathered} y=mx+b \\ \\ \text{where m is the rate of change or slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Comparing the function given to the general form of a linear equation,
[tex]\begin{gathered} P(n)=415n-10790 \\ y=mx+b \\ \\ m=415 \\ b=-10790 \end{gathered}[/tex]Therefore,
The rate of change is $415.00 per computer.
The company earns $415.00 per computer sold.
The initial value is the y-intercept. This is the point when no computer has been sold yet.
[tex]\begin{gathered} \text{when n = 0} \\ P(n)=415n-10790 \\ P(0)=415(0)-10790 \\ P(0)=-10790 \end{gathered}[/tex]Therefore,
The initial value is $-10790.00
If the company sells 0 computers, they will not make a profit. They will lose $10790.00
P(44) means the profit made when 44 computers are sold.
[tex]\begin{gathered} \text{when n = }44 \\ P(n)=415n-10790 \\ P(44)=415(44)-10790 \\ P(44)=18260-10790 \\ P(44)=7470 \end{gathered}[/tex]
Therefore,
The company will earn $7470.00 if they sell 44 computers.
P(n) = 13280
[tex]\begin{gathered} \text{when P(n) = }13280 \\ P(n)=415n-10790 \\ 13280=415n-10790 \\ 13280+10790=415n \\ 24070=415n \\ \text{Dividing both sides by 415,} \\ \frac{24070}{415}=n \\ n=58 \end{gathered}[/tex]
Therefore,
The company will earn $13280.00 if they sell 58 computers.
