Suppose the half life of carbon 14 is 5730 years Write an eq

Suppose the half life of carbon 14 is 5730 years. Write an equation for P(t), the percentage of carbon 14 remaining after t years of radioactive decay.

Also, write an equation for continuous decay of carbon 14.

Solution

We have to use the following formula

P(t)=P₀e^kt

At half life

P(t)=(1/2)P₀

So we get

(1/2)P₀=P₀e^5730k

1/2=e^5730k

taking ln on both sides

ln .5= 5730k

k=(ln.5)/5730

Required equation is

P(t)=P₀e^t(ln.5)/5730

P(t)=P₀(.5)^t/5730