I need a clear explanation please bc i don't get how I'm supposed to do this. :,)

The half-life is the amount of time it takes for some quantity of carbon-14 to decay to half the original amount, or .

In terms of the formula, it's the time such that

and we can divide both sides by the original amount to get

We want to find the time it takes for 57%, or 0.57, of the original amount to remain. This means we solve for in

or

We're given ; plug this in and solve for :

1. 2

2. 11

3. 5

4. 6

5. 7

6. 5

7. -1

8. 1

step-by-step explanation: