carbon - 14 is an element that loses about 10% of its mass every millennium (i.e., 1000 years). a sample of…

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 samples mass in grams, $s(t)$, $t$ millennia from today. $s(t)=$

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 samples mass in grams, $s(t)$, $t$ millennia from today. $s(t)=$

Answer

Explanation:

Step1: Identify the initial - value and decay factor

The initial mass of the Carbon - 14 sample is $a = 600$ grams. Since it loses 10% of its mass every millennium, the remaining mass is 90% or 0.9 of the previous mass. So the decay factor $b=0.9$.

Step2: Write the exponential - decay function

The general form of an exponential - decay function is $S(t)=a\times b^{t}$, where $a$ is the initial amount, $b$ is the decay factor, and $t$ is the number of time - periods. Substituting $a = 600$ and $b = 0.9$ into the formula, we get $S(t)=600\times(0.9)^{t}$.

Answer:

$S(t)=600\times(0.9)^{t}$