Finding exponential decay given half-life problem

Question

The half-life of a certain radioactive substance is 10 years. Initially there are 100 grams of the substance. Let A(t) be the number of grams of the substance at time t years. Find each of the following function values.

a. A(0)

b. A(20)

c. A(60)

d. A(t)

e. A(10)

Answer 1

Half-life problems have the format of:

    A(t) = A(0) (1/2) ^t/t1/2             where A(0) is the starting amount (or the amount when t = 0)

With the given information that A(0) is 100g (initial amount) and t_½ is 10 years:

    A(t) = 100 g (1/2) ^t/10            

Thus:

    A(0) = 100 g (1/2)^0/10 = 100 g

    A(20) = 100 g (1/2)^20/10 = 25 g

    A(60) = 100 g (1/2)^60/10 = 1.5625 g

    A(t) = 100 g (1/2) ^t/10  

    A(10) = 100 g (1/2) ^10/10 = 50 g