Question

Einsteinium-253 is an element that loses about 2/3 of its mass every month. A sample of Einsteinium-253 has 450 grams. Write a function that gives the sample's mass in grams, S(t),t months from today.

Answer 1

The function $S(t)=450(\dfrac{1}{3})^t$ would give the sample's mass in grams after t  months.

Step-by-step explanation:

Given,

Original quantity of the element the einsteinium-253 = 450 grams

Since it is losing 2/3 of its mass every month,

Initial part = 1,

Loss = 2/3

Remaining = $1-\frac{2}{3}=\frac{1}{3}$

Thus, its quantity in each month is 1/3 of the quantity in previous month.

So, after 1 month, its quantity = $\frac{450}{3}=450(\frac{1}{3})$

After 2 months = $450(\frac{1}{3})(\frac{1}{3})=450(\frac{1}{3})^2$

After 3 months = $450(\frac{1}{3})^3$

........so on..

Hence, after t months its quantity( say S(t) ) is,

$S(t)=450(\frac{1}{3})^t$

Which is the required function.

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