Answer :
Answer:
You will have 1.585 left after 35 years.
Step-by-step explanation:
Equation for amount of a substance:
The equation for the amount of a substance, using exponential decay, is given by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
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 [tex]A(15) = 0.5A(0)[/tex]. We use this to find r.
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]0.5A(0) = A(0)(1 - r)^{15}[/tex]
[tex](1 - r)^{15} = 0.5[/tex]
[tex]\sqrt[15]{(1 - r)^{15}} = \sqrt[15]{0.5}[/tex]
[tex]1 - r = (0.5)^{\frac{1}{15}}[/tex]
[tex]1 - r = 0.9548[/tex]
Then
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = A(0)(0.9548)^t[/tex]
You have 8 ounces of this strange substance today
This means that [tex]A(0) = 8[/tex]. So
[tex]A(t) = A(0)(0.9548)^t[/tex]
[tex]A(t) = 8(0.9548)^t[/tex]
How much will you have left after 35 years?
This is A(35). So
[tex]A(t) = 8(0.9548)^t[/tex]
[tex]A(35) = 8(0.9548)^{35} = 1.585[/tex]
You will have 1.585 left after 35 years.