Question

The sample loses 1/3of it’s mass every ___ days

Answer 1

The sample loses
`(1)/(3)` of its mass every
`(1)/(3)` days.

Explanation:

Expression that shows the relation between final mass of the element after 't' days is,

M(t) =
`900((8)/(27))^t`

If M(t) = two third of the initial mass [After the loss of one third of the initial mass remaining mass of the element = 1 -
`(1)/(3)` =
`(2)/(3)`rd of the initial mass]

`900* (2)/(3)=900((8)/(27))^t`

`(2)/(3)=((8)/(27))^t`

`(2)/(3)=[((2)/(3))^3]^t`

`((2)/(3))^1=((2)/(3))^(3t)`

By comparing powers on both the sides

3t = 1

t =
`(1)/(3)` day

Therefore, The sample loses
`(1)/(3)` of its mass every
`(1)/(3)` days.