Question

The half-life is the time it takes for only half of something to remain. For example, if there are 100 atoms, after one half-life time period, 50 atoms remain. At the beginning of a time period, there are 16 atoms of a radioactive substance. Which table shows the correct equations and number of atoms of the substance remaining after each half-life time period, x, passes?

Answer 1

First we define the variable to be used:
 x: half-life time period
 The equation for this problem can be modeled as:
 y = A * (b) ^ x
 Where,
 A: initial amount
 b: decrease rate.
 For example:
 if there are 100 atoms, after one half-life time period, 50 atoms remain:
 y = 100 * (0.50) ^ x
 after one half-life time period (x = 1):
 y = 100 * (0.50) ^ 1
 y = 50
 The equation that models the problem is:
 y = 16 * (0.50) ^ x
 The table is:
 1     8
 2     4
 3     2
 4     1
 5     0.5