Question

Einsteinium-
253
253253 is an element that loses about
2
3
3
2
​
start fraction, 2, divided by, 3, end fraction of its mass every month. A sample of Einsteinium-
253
253253 has
450
450450 grams.
Write a function that gives the sample's mass in grams,
S
(
t
)
S(t)S, left parenthesis, t, right parenthesis,
t
tt months from today.
S
(
t
)
=

Answer 1

Answer:

                 $S(t)=450(2/3)^t$

Explanation:

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

Since einstenium-253 loses about 2/3 of its mass every month, you can model the amount of sample by an exponential decay function, which is a geometric progression with a growing factor less than 1.

The general form of an exponential decay function is:

$y=A_0r^t$

Where:

• A₀ is the initial value
• r is the growing or decaying factor
• t is the time
• y is the value of the function at time t.

In this case, you have:

• A₀ = 450
• r = 2/3
• t = t
• y = S(t)

Now you can replace the values in the model and will obtain:

                  $S(t)=450(2/3)^t$