Question

A rock has 25 percent of its original amount of potassium-40 remaining in it; potassium-40 has a half-life of 1.25 billion years. How long ago was the rock formed?

1.25 billion years ago

2.50 billion years ago

5.00 billion years ago

6.25 billion years ago

Answer 1

sorry for waiting :D

Answer 2

How many times can you cut something in half before you're left with 25% of what you started with?

Answer 3

2, So, the "cutting in half" is the same thing as a half-life. Half-lives always leave behind half of what was present at the start of that half-life. Leaving 25% means that 2 half-lives have passed.

Answer 4

Nt = 25/100 No
Nt/No = 25/100 = 1/4

1/4 = (1/2)^(t/1.25)
t = 2.5

Answer 5

So, since you know 2 half-lives have passed, and you know how long each half-life is, you can easily find out how long ago the rock was made (when it had 100% remaining, before any half-lives passed)

Answer 6

Since each half-life is 1.25 billion years, and 2 half-lives must have passed, how old is the rock?

2.5