Solve the problem.
-In the formula A $$\mathrm { A } = \mathrm { Ie }^{ { kt }}$$ A is the amount of radioactive material remaining from an initial amount I at a given time t and k is a negative constant determined by the nature of the material. A certain radioactive isotope has a
Half-life of approximately 1450 years. How many years would be required for a given amount of this isotope to
Decay to 60% of that amount?
A) 1069 yr
B) 580 yr
C) 1009 yr
D) 1917 yr

Question

Quizplus · Accepted Answer

The formula for decay based on half-life is $A = Ie^{kt}$. Given that the half-life is 1450 years, we can find $k$ by setting $A = \frac{I}{2}$ and $t = 1450$, leading to $\frac{1}{2} = e^{1450k}$. Solving for $k$ gives us a specific value. To find the time $t$ when $A = 0.6I$, we substitute $k$ and solve $0.6 = e^{kt}$. The correct calculation will show that it takes approximately 1069 years for the isotope to decay to 60% of its original amount.

Solve the Problem A=Iekt\mathrm { A } = \mathrm { Ie }^{ { kt }}A=Iekt

Solve the Problem $\mathrm { A } = \mathrm { Ie }^{ { kt }}$