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. Which graph shows the sample's mass yyy (in grams) after xxx millennia?

Answer 1

S(t)=600(0.9)

Explanation:

Losing mass at a rate of 10\%10%10, percent per millennium means the sample keeps 100\%-10\%=90\%100%−10%=90%100, percent, minus, 10, percent, equals, 90, percent of its mass each millennium.

So each millennium, the size is multiplied by 90\%90%90, percent, which is the same as a factor of 0.90.90, point, 9.

If we start with the initial mass, 600600600 grams, and keep multiplying by 0.90.90, point, 9, this function gives us the mass of the sample ttt millennia from now:

S(t)=600(0.9)^tS(t)=600(0.9)

t

Answer 2

Carbon-14 loses around 10% ( 0.1 in decimal form) of its mass, after one millennium.

Then if we start with a mass A of Carbon-14, after one millennium we will have a mass equal to:

A - A*0.1 = A*(0.9)

After another millennium, we will have a mass equal to:

A*(0.9) - A*(0.9)*0.1 = A*(0.9)^2

And so on, this is an exponential decay.

We already can see the pattern here, after x millenniums, the mass of carbon-14 will be:

M(x) = A*(0.9)^x

Now, in this problem we have 600 grams of carbon-14, then the equation for the mass will be:

y = M(x) = 600g*(0.9)^x

And the graph of this equation is shown below.