Question

linear functions application
identify the information given to you in the application problem below.
use that information to answer the questions that follow.
round your answers to two decimal places as needed.
the function $p(n)=495n - 10395$ represents a computer manufacturers profit $p(n)$ when $n$ computers are sold.
identify the rate of change, and complete the following sentence to explain its meaning in this situation.
rate of change: 495
the company earns $495 per computer sold.
identify the initial value, and complete the following sentence to explain its meaning in this situation.
initial value = 10395
if the company sells 0 computers, they will not make a profit. they will lose $10395.
evaluate $p(46)$.
complete the following sentence to explain the meaning of your answer.
the company will earn $12375 if they sell 46 computers.
find the value of $n$ where $p(n)=20790$.
complete the following sentence to explain the meaning of your answer.
the company will earn $20790 if they sell 63 computers.
question help: video

Explanation:

Step1: Recall linear - function form

The linear function is $P(n)=495n - 10395$, which is in the form $y = mx + b$ where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value).

Step2: Identify rate of change

For $P(n)=495n - 10395$, the coefficient of $n$ is 495. So the rate of change is 495. It means the company earns $495 per computer sold.

Step3: Identify initial value

When $n = 0$, $P(0)=495\times0-10395=- 10395$. The initial value is - 10395. It means if the company sells 0 computers, they will lose $10395.

Step4: Evaluate $P(46)$

Substitute $n = 46$ into $P(n)=495n - 10395$. So $P(46)=495\times46-10395=22770 - 10395=12375$. It means the company will earn $12375 if they sell 46 computers.

Step5: Solve for $n$ when $P(n)=20790$

Set $495n-10395 = 20790$. Add 10395 to both sides: $495n=20790 + 10395=31185$. Then divide both sides by 495: $n=\frac{31185}{495}=63$. It means the company will earn $20790 if they sell 63 computers.

Answer:

Rate of Change: 495; The company earns $495 per computer sold.
Initial value: - 10395; If the company sells 0 computers, they will lose $10395.
$P(46)=12375$; The company will earn $12375 if they sell 46 computers.
$n = 63$ when $P(n)=20790$; The company will earn $20790 if they sell 63 computers.