Question

A balloon with a snail leak loses 0.5% of its volume each day.If it originally contained 40 liters of gas,what is the volume of the gas after one week?

Answer 1

The initial volume is 40 liters.

The volume lost on first day is,

`40\cdot(0.5)/(100)=40\cdot0.005`

The volume left after first day leak is,

`\begin{gathered} 40-40\cdot0.005=40(1-0.005) \\ =40(0.995) \end{gathered}`

The volume leak on second day is,

`40(0.995)\cdot(0.5)/(100)=40(0.995)\cdot0.005`

The volume left after second day leak is,

`\begin{gathered} 40(0.995)-40(0.995)(0.005)=40(0.995)(1-0.005) \\ =40(0.995)\cdot(0.995) \\ =40\cdot(0.995)^2 \end{gathered}`

In same manner if volume decreases for seven days, then volume of gas is,

`40\cdot(0.995)^7`

Answer: Option D