Solve the problem.
-A certain radioactive isotope has a half-life of approximately 1900 years. How many years to the nearest year would be required for a given amount of this isotope to decay to $55 \%$ of that amount?
A) 1584 years
B) 1639 years
C) 855 years
D) 2189 years

Question

Quizplus · Accepted Answer

The decay of a radioactive isotope can be modeled using the formula $ N(t) = N_0 \times (0.5)^{t/T} $, where $ N(t) $ is the remaining quantity, $ N_0 $ is the initial quantity, $ t $ is the time, and $ T $ is the half-life. Setting $ N(t)/N_0 = 0.55 $ and $ T = 1900 $, solve for $ t $: $ 0.55 = (0.5)^{t/1900} $. Taking the logarithm of both sides and solving for $ t $ gives approximately 1639 years.

Solve the Problem 55%55 \%55% Of That Amount? A) 1584 Years B) 1639 Years C)

Solve the Problem $55 \%$ Of That Amount?
A) 1584 Years
B) 1639 Years
C)