Question

A radioactive substance decays according to the formula

Q(t)=Q0eâkt where Q(t) denotes the amount of the substance present at time t (measured in years),
Q0 denotes the amount of the substance present initially, and k (a positive constant) is the decay constant.
(a) Find the half-life of the substance in terms of k.
(b) Suppose a radioactive substance decays according to the formula
Q(t)=15eâ0.0001438t
How long will it take for the substance to decay to half the original amount? (Round your answer to the nearest whole number.) yr

Answer 1

`t=4820 y`

Explanation:

a) The half-life equation is given by:

`t_(1/2)=(ln(2))/(k)`

b) Using the decay equation we have:

`Q(t)=15e^(-0.0001438t)`

we need to find t when
`Q(t)=(Q_(0))/(2)`

`7.5=15e^(-0.0001438t)`

`0.5=e^(-0.0001438t)`

`ln(0.5)=-0.0001438t`

`t=(ln(0.5))/(-0.0001438)`

`t=4820 y`

Therefore, it will take 4820 years to decay to half the original amount.

I hope it helps you!