The function that gives the sample's mass after t millennia can be derived
from the equation for decreasing rate formula.
Reasons:
The rate at which carbon-14 loses its mass = 10% per millennium
The initial mass of the sample of carbon-14 = 600 grams
Required:
A function that gives the mass of the sample in grams S(t), in t millennia
from today.
Solution:
The formula for decreasing rate is; y = a·(1 - r)ˣ
Where:
y = S(t) = The mass of the sample after t millennia
x = t = The number of millennia
a = Initial mass = 600 grams
r = The decay rate = 10% = 0.1
By plugging in the above values, we get;
[tex]S(t) = 600 \cdot (1 - 0.1)^t = \mathbf{600 \cdot (0.9)^t}[/tex]
[tex]Therefore, \ the \ function \ is; \underline{S(t) = 600 \cdot (0.9)^t}[/tex]
Lear1n more about the expression for the rate of decrease here:
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