Solve the following exponential application problem involving half life of a substance. Plutonium-239 has a half-life of 24,000 years. A rule of...

You haven't been able to understand the response I gave
you earlier. Let me try to clarify. Plutonium 239 has a half life of 24000 years. Half
life is the duration of time required for the initial amount of a substance to reduce to
1/2 the amount. Plutonium is virtually harmless after 10 half lives. After 10 half
lives, the initial amount reduces to 1/(2^10).

Now if you
want to use the equation you have, you have to plug in the value A0*(1/2)^10 as the
final amount.

This gives A0(1/2)^10 = A0*2^(-t/
24000)

=> (1/2)^10 =
2^(-t/24000)

=> 2^10 =
2^(t/24000)

=> 10 =
t/24000

=> t =
10*24000

=> t =
240000

But here you are actually using the answer to create
the value that has to be used in the equation and then using the equation to get back
the same value that started with initially.

Instead of
doing all this, you should learn when to use the equation and when that is not required.
Here, the use of the equation is not required as you can write the answer straight away
from the information provided.