hannahelisabeth19
15.04.2020 •
Mathematics
Nickel-63 is a radioactive substance with a half-life of about 100 years. An artifact had
9.8 milligrams of nickel-63 when it was first measured. Write an equation to represent
the mass of nickel-63, in milligrams, as a function of:
a. tt, time in years
b. dd, time in days
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Ответ:
a) x = 9.8 × 0.5^(t/100)
b) x = 9.8 × 0.5^(d/36500)
Step-by-step explanation:
a) x = 9.8 × 0.5^(t/100)
100 years = 365×100 days
= 36500 days
b) x = 9.8 × 0.5^(d/36500)
Ответ:
see below
Step-by-step explanation:
The equation for half life is
n = no e ^ (-kt)
Where no is the initial amount of a substance , k is the constant of decay and t is the time
no = 9.8
1/2 of that amount is 4.9 so n = 4.9 and t = 100 years
4.9 = 9.8 e^ (-k 100)
Divide each side by 9.8
1/2 = e ^ -100k
Take the natural log of each side
ln(1/2) = ln(e^(-100k))
ln(1/2) = -100k
Divide each side by -100
-ln(.5)/100 = k
Our equation in years is
n = 9.8 e ^ (ln.5)/100 t)
Approximating ln(.5)/100 =-.006931472
n = 9.8 e^(-.006931472 t) when t is in years
Now changing to days
100 years = 100*365 days/year
36500 days
Substituting this in for t
4.9 = 9.8 e^ (-k 36500)
Take the natural log of each side
ln(1/2) = ln(e^(-36500k))
ln(1/2) = -36500k
Divide each side by -100
-ln(.5)/36500 = k
Our equation in years is
n = 9.8 e ^ (ln.5)/36500 d)
Approximating ln(.5)/365=-.00001899
n = 9.8 e^(-.00001899 d) when d is in days
Ответ:
80
Step-by-step explanation:
just did it on calculator
:>