Question

given the graph is of f(x)
a certain company makes money determined by the function p(u)=\frac{1}{4}u^{2}-2u, where u = units of incense sold and p = profit
a. read the notation.
b. find p(8).
c. what does p(8) mean?
d. what does p(u)=86,000 mean?

Explanation:

Step1: Analyze the function - reading notation

The notation $P(u)$ represents a function where $u$ is the input (units of incense sold) and $P$ is the output (profit).

Step2: Calculate $P(8)$

Substitute $u = 8$ into $P(u)=\frac{1}{4}u^{2}-2u$.
$P(8)=\frac{1}{4}\times8^{2}-2\times8$
$=\frac{1}{4}\times64 - 16$
$=16 - 16$
$=0$

Step3: Interpret $P(8)$

$P(8)$ means the profit of the company when 8 units of incense are sold. Since $P(8)=0$, the company breaks - even (makes no profit or loss) when 8 units of incense are sold.

Step4: Interpret $P(u)=86000$

$P(u) = 86000$ means that the profit of the company is 86000 when $u$ units of incense are sold. We would need to solve the equation $\frac{1}{4}u^{2}-2u=86000$ to find the value of $u$.

Answer:

a. $P(u)$ is a function where $u$ is units of incense sold and $P$ is profit.
b. $P(8)=0$
c. The profit of the company when 8 units of incense are sold.
d. The profit of the company is 86000 when $u$ units of incense are sold.