Question

Each month, you start with $2$ gigabytes of data and use $0.08$ gigabyte per day. The table shows the amount $\mathrm{y}$ of data that your friend has left $\mathrm{x}$ days after the start of each month. Who runs out of data first $?$

Answer 1

Step 1: Finding when i will finish $2$ gigabytes data.

Given, I am starting with $2$ gigabytes of data .

I used $0.08$ gigabyte per day so, I will finish $2$ gigabytes in,

$\frac{20}{0.08}$

$=25$ days

Step 2: Finding when friend will finish $3$ gigabytes data.

For friend lets make function from table.

From the table, ordered pair $(0,3)(7,2.3)(14,1.6)$

Function, $\mathrm{y}=-0.1\mathrm{x}+3$(From table)

Lets find $\mathrm{x}$-intercepts,

So, $\mathrm{y}=0$

$$\begin{gathered} \Rightarrow 0=-0.1\mathrm{x}+3 \\ \Rightarrow 0.1\mathrm{x}=3 \\ \Rightarrow \mathrm{x}=\frac{3}{0.1} \\ \Rightarrow \mathrm{x}=30 \end{gathered}$$

Friend will finish data in $30$ days.

Hence, I am running out of my data first.