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

Answer:

$t=4820 y$

Step-by-step explanation:

a) The half-life equation is given by:

$t_{1/2}=\frac{ln(2)}{k}$

b) Using the decay equation we have:

$Q(t)=15e^{-0.0001438t}$

we need to find t when $Q(t)=\frac{Q_{0}}{2}$

$7.5=15e^{-0.0001438t}$

$0.5=e^{-0.0001438t}$

$ln(0.5)=-0.0001438t$

$t=\frac{ln(0.5)}{-0.0001438}$

$t=4820 y$

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

I hope it helps you!