Question

a wireless phone company has a pricing scheme that includes 250 minutes worth of phone usage in the basic $35. each minute over and above the first 250 minutes of usage is charged at $0.40 per minute. a. let $x$ be the number of minutes of phone usage per month. what is the expression for the average cost per minutes if the value of $x$ is between 0 and 250? b. what is the expression for the average cost per minute if the value of $x$ is in the interval $(250,300$. c. if phone usage in a certain month is 300 minutes, what is the average cost per minute. round to the nearest cent. question help: ebook written example

Explanation:

Step1: Calculate cost for part - a

The basic cost is $35$ and there is no additional charge for $0\leq x\leq250$. The average cost per minute $\overline{C}(x)=\frac{35}{x}$ for $0 < x\leq250$.

Step2: Calculate cost for part - b

For $250 < x\leq300$, the basic cost is $35$ and the additional cost for $(x - 250)$ minutes is $0.4(x - 250)$. The total cost $C=35+0.4(x - 250)=35 + 0.4x-100=0.4x - 65$. The average cost per minute $\overline{C}(x)=\frac{0.4x - 65}{x}=0.4-\frac{65}{x}$ for $250 < x\leq300$.

Step3: Calculate cost for part - c

When $x = 300$, we use the formula from part - b. $\overline{C}(300)=0.4-\frac{65}{300}=0.4 - 0.2167\approx0.1833\approx18$ cents.

Answer:

a. $\overline{C}(x)=\frac{35}{x},0 < x\leq250$
b. $\overline{C}(x)=0.4-\frac{65}{x},250 < x\leq300$
c. $18$ cents