The half-life of a radioactive substance is 28.1 years.

Question

The​ half-life of a radioactive substance is

28.1

years.

a. Find the exponential decay model for this substance.

b. How much of the sample of

1000

grams will remain after

10

​years?

c. How long will it take a sample of

1000

grams to decay to

900

​grams?

Answer 1

(a)

m₀ = initial amount

t = years

m(t) = m₀ (0.5)^t/28.1

(b)

m(10) = 1000 (0.5)^10/28.1 g = ? g

(c)

900 = 1000 (0.5)^t/28.1

0.9 = (0.5)^t/28.1

log0.9 = (t/28.1) log0.5

Solve for t and finish from here. Work with any base for the logs, as long as it is the same for both. The result will be in years.