Question

Carbon-141414 is an element that loses about 10\%10%10, percent of its mass every millennium (i.e., 100010001000 years). A sample of Carbon-141414 has 600600600 grams.

Write a function that gives the sample's mass in grams, S(t)S(t)S, left parenthesis, t, right parenthesis, ttt millennia from today.

Answer 1

S(t) = 600*0.9^t

Explanation:

Answer 2

S(t) = 600*0.9^t

Explanation:

At the beginning (t = 0) the sample has 600 grams. After 1 millennium from today (t = 1) the mass will be: 600 - 600*0.1 = 600*0.9. After 2 millennium from today (t = 2) the mass will be the 90% of the mass in the previous millenium, that is: 600*0.9*0.9 = 600*0.9^2. Analogously, at time = 3, sample's mass will be: 600*0.9^2*0.9 = 600*0.9^3. In a table format, that is

t m

0 600

1 600 - 600*0.1 = 600*0.9

2 600*0.9*0.9 = 600*0.9^2

3 600*0.9^2*0.9 = 600*0.9^3

Therefore, sample's mass in grams, S(t), where t refers to millennia from today is computed as follows: S(t) = 600*0.9^t