Question

2. A 175g sample of radioactive kryptonite-344 has a half-life of 122 days.

a) Write the exponential equation that gives the amount of kryptonite that remains after t days.

Write equation in the form M(t)= ab* where x=

elapsed time

half-life time

Answer 1

`M(t) = 175(0.9943)^(t)`

Explanation:

The amount of kryptonite-344 after t days is given by the following equation:

`M(t) = ab^(t)`

In which a is the initial amount.

175g sample:

This means that
`a = 175`

So

`M(t) = 175b^(t)`

Half-life of 122 days.

This means that
`M(122) = 0.5*175 = 87.5`

So

`M(t) = 175b^(t)`

`87.5 = 175b^(122)`

`b^(122) = 0.5`

`\sqrt[122]{b^(122)} = \sqrt[122]{0.5}`

`b = 0.9943`

So

`M(t) = 175(0.9943)^(t)`