Question

"Demetrius' local cell phone company charges for how much data he uses each month. The first 10 GB of data he uses costs $3 per GB. Once he exceeds the 10 GB, the company then charges $15 for each GB after. "

Answer 1

Given:

The first 10 GB of data costs $3 per GB.

After exceeds 10 GB, the company charges $15 for each GB.

Required:

We need to find the function for the given situation.

Step-by-step explanation:

Let x be the number of GB that "Demetrius' used.

Let f(x) be the cost.

The first 10 GB of data costs $3 per GB.

`\text{The first 10 Gb can be written as }0\leq x\leq10.`
`f(x)=3x\text{ if }0\leq x\leq10.`

After exceeding 10 GB, the company charges $15 for each GB

`After\text{ exceeding 10 GB can be written as }x>!0`
`f(x)=15x\text{ if }x>10`

Final answer:

`f(x)=\begin{cases}{3x\text{ if }0\leq x\leq10.} \\ {15x\text{ if }x>10.}\end{cases}`