A graph depicting exponential decay is concave up, as evidenced by the positive second derivative of the decay function. Here option B is correct.
A graph showing exponential decay is concave up, not concave down. Exponential decay is characterized by a process in which a quantity decreases over time, and its rate of decrease is proportional to its current value.
Mathematically, it is represented by a function of the form
, where (a) is the initial quantity, (b) is a positive constant determining the decay rate, (x) is time, and (e) is the base of the natural logarithm.
The second derivative of this function, which determines concavity, is positive, indicating a concave-up shape. The concave-up nature of exponential decay graphs reflects the acceleration of the decay rate as the quantity decreases.
In contrast, a concave-down graph would suggest a decelerating decay rate, which is not characteristic of exponential decay. Therefore, the correct answer is (b) false.