Respuesta :
After 17190 years, Carbon-14 will reach a mass of 15 grams.
Pi is your initial amount (120 grams)
0.5 as your exponential base represents your HALF life hence 0.5
t represents the time elapsed
c represents your given half life value of (5730)
P(t) represents the exponential function of your half life
120/2 =60
60/2 = 30
30 /2 = 15
As you can see above, 3 half lives of 5730 years EACH degraded the carbon-14 to 15 grams. You divide each number by two as it is a HALF life.
P(t)= Pi (0.5) ^t/c
P(17190) = 120 (0.5) ^17190/5730
P(17190) = 120 (0.5) ^3
P(17190) = 15 grams
So your answers should be 3 half lives or after 17190 years have elapsed!
Pi is your initial amount (120 grams)
0.5 as your exponential base represents your HALF life hence 0.5
t represents the time elapsed
c represents your given half life value of (5730)
P(t) represents the exponential function of your half life
120/2 =60
60/2 = 30
30 /2 = 15
As you can see above, 3 half lives of 5730 years EACH degraded the carbon-14 to 15 grams. You divide each number by two as it is a HALF life.
P(t)= Pi (0.5) ^t/c
P(17190) = 120 (0.5) ^17190/5730
P(17190) = 120 (0.5) ^3
P(17190) = 15 grams
So your answers should be 3 half lives or after 17190 years have elapsed!
Carbon-14 has a half-life of 5,730 years. After 4 half-lives will 120 grams of Carbon-14 decay to 15 grams. Option D is correct.
what is half life?
The half-life of a substance (atoms, molecules, or ions) refers to the time it takes for half of its given amount to radioactively decay. The rate at which reactants are converted into products is proportional to the concentration of reactants present.
carbon-14 has a half-life of 5730 years.
half life = total number of amount / total number of half-life
substituting the value in the equation,
120 g of carbon decay in 5730 years
15 g of carbon will decay= 120/4
= 15
So, 4 is the number of half-lives in which the 120 g of carbon will decay.
Therefore, the 120g of carbon needs 4 life to be 15g.
Learn more about half-life, here;
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