A radioactive element, actinium, has a half-life of 4 seconds. You begin with 60 grams of actinium. a) Write an exponential equation describing the amount you would have left after t seconds.

Question

A radioactive element, actinium, has a half-life of 4 seconds. You begin with 60

grams of actinium.

a) Write an exponential equation describing the amount you would have left after t seconds.

b) Use the model to calculate how much will remain after 36 seconds.

c) What percent of the original mass is left after 20 seconds?

Answer 1

(a)

m(t) = m₀ (0.5)^t/4

m₀ = 60 g

t = seconds from when m was 60 g

m(t) = 60 (0.5)^t/4 (in grams)

(b)

Plug t=36 into the equation and evaluate m(36).

(c)

Plug in t=20 into the equation and evaluate m(20). The percent remaining will be

100 m(20) / m₀ = 100 m(20) / 60