Question

Solution:

Answer 1

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:

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

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.

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

$0.5A(0) = A(0)(1 - r)^{15}$

$(1 - r)^{15} = 0.5$

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

$1 - r = (0.5)^{\frac{1}{15}}$

$1 - r = 0.9548$

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.