MATH SOLVE

2 months ago

Q:
# 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?

Accepted Solution

A:

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

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