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

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)

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