Question

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

Answer 1

Answer:

The sample loses $\frac{1}{3}$ of its mass every $\frac{1}{3}$ days.

Step-by-step explanation:

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

M(t) = $900(\frac{8}{27})^t$

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 - $\frac{1}{3}$ = $\frac{2}{3}$rd of the initial mass]

$900\times \frac{2}{3}=900(\frac{8}{27})^t$

$\frac{2}{3}=(\frac{8}{27})^t$

$\frac{2}{3}=[(\frac{2}{3})^3]^t$

$(\frac{2}{3})^1=(\frac{2}{3})^{3t}$

By comparing powers on both the sides

3t = 1

t = $\frac{1}{3}$ day

Therefore, The sample loses $\frac{1}{3}$ of its mass every $\frac{1}{3}$ days.