The​ half-life of a certain radioactive element is about

Question

1500 years. After
2800 ​years, what percentage P of a sample of this element​ remains?

Answer 1

you have to multiply by 1/2 every 1500 years. So, the fraction remaining after t years is

(1/2)^(t/1500)

So, after 2800 years, the fraction remaining is

(1/2)^(2800/1500) = 2^-1.8667 = 0.2742 = 27.42%

Note that 2800 is almost 3000, or two half-lives. At t=3000, 1/2^2 = 1/4 = 0.25 will be left. So, we haven't quite reached that level yet.

Answer 2

what is 100*e^(-.692*2800/1500) ?

Put this in your google search window:
100*e^(-.692*28/15)=