The model describes the amount of Cesium-137 remaining after t years. Which one of the following written statements best describes the behavior of Cesium-137?
A) The amount of radioactive substance decreases by half every years.
B) The amount of radioactive substance increases by half every year.
C) The amount of radioactive substance increases by half every years.
D) The amount of radioactive substance decreases by half every 79 years.
E) The amount of radioactive substance decreases by half every year.

Question

The model  describes the amount of Cesium-137 remaining after t years. Which one of the following written statements best describes the behavior of Cesium-137?
A) The amount of radioactive substance decreases by half every years. 
B) The amount of radioactive substance increases by half every year. 
C) The amount of radioactive substance increases by half every years. 
D) The amount of radioactive substance decreases by half every 79 years. 
E) The amount of radioactive substance decreases by half every year.

Quizplus · Accepted Answer

The model 11ec1b6e_3c4d_b297_bbf8_7337aba085d0_TBX8728_00 is an exponential decay function of the form A(t) = A0*e^(-kt) where A0 is the initial amount, t is time in years, k is the decay constant, and A(t) is the amount remaining after t years. The fact that it decreases by half is a characteristic of exponential decay. The formula for the time it takes for an exponential decay to decrease by half is t1/2 = ln(2)/k, where ln is the natural logarithm. Plugging in the given value of t1/2 = 79, we can solve for k to get k = ln(2)/79. Therefore, the correct statement is that the amount of radioactive substance decreases by half every 79 years.

The Model Describes the Amount of Cesium-137 Remaining After