Solve.
-In the formula A = Iekt, 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
Decays at a rate of 0.3% annually. Determine the half-life of this isotope, to the nearest year.
A) 167 yr
B) 100 yr
C) 2 yr
D) 231 yr

Question

Quizplus · Accepted Answer

The half-life of a radioactive isotope is found by setting A = 1/2I in the formula A = Ie^(kt) and solving for t. Given the decay rate of 0.3% annually, k = -0.003. To find the half-life, we set up the equation 1/2 = e^(-0.003t). Taking the natural logarithm of both sides gives ln(1/2) = -0.003t. Solving for t gives t ≈ 231 years.

Solve. -In the Formula a = Iekt, a Is the Amount