Mathematics: Carbon-14 is an element that loses about 10% of its mass every millennium (i.e., 1000 years). a sample of carbon-14 has 600 grams. write a function that gives the sample’s mass in grams, s(t), t millennia from today.

Area=Length*BreadthStep-by-step explanation:...

Carbon-14 is an element that loses about 10% of

anitadefrances

09.01.2022

The function that gives the sample's mass after t millennia can be derived

from the equation for decreasing rate formula.

The mass of the sample after t millennia is; $\underline{S(t) = 600 \cdot (0.9)^t}$

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;

$S(t) = 600 \cdot (1 - 0.1)^t = \mathbf{600 \cdot (0.9)^t}$

$Therefore, \ the \ function \ is; \underline{S(t) = 600 \cdot (0.9)^t}$

Lear1n more about the expression for the rate of decrease here:

link

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