Question

Solution:

2. The half-life of BRADIUM-29 is 15 years. If you have 8 ounces of this strange substance today, how much will you
have left after 35 years?
题
SKU

Answer 1

You will have 1.585 left after 35 years.

Explanation:

Equation for amount of a substance:

The equation for the amount of a substance, using exponential decay, is given by:

`A(t) = A(0)(1 - r)^t`

In which A(0) is the initial amount and r is the decay rate, as a decimal.

The half-life of BRADIUM-29 is 15 years.

This means that
`A(15) = 0.5A(0)`. We use this to find r.

`A(t) = A(0)(1 - r)^t`

`0.5A(0) = A(0)(1 - r)^(15)`

`(1 - r)^(15) = 0.5`

`\sqrt[15]{(1 - r)^(15)} = \sqrt[15]{0.5}`

`1 - r = (0.5)^{(1)/(15)}`

`1 - r = 0.9548`

Then

`A(t) = A(0)(1 - r)^t`

`A(t) = A(0)(0.9548)^t`

You have 8 ounces of this strange substance today

This means that
`A(0) = 8`. So

`A(t) = A(0)(0.9548)^t`

`A(t) = 8(0.9548)^t`

How much will you have left after 35 years?

This is A(35). So

`A(t) = 8(0.9548)^t`

`A(35) = 8(0.9548)^(35) = 1.585`

You will have 1.585 left after 35 years.