Final Answer:
The graph of the function modeling the decay of rhodium-101 will continue to decrease exponentially as 100 more years pass, showing a further decline in the quantity of the substance.
Step-by-step explanation:
Rhodium-101 undergoes radioactive decay, where its quantity decreases over time. The function representing radioactive decay typically follows an exponential decay model, given by the equation N(t) = N0 * e^(-kt), where N(t) represents the quantity of the substance at time t, N0 is the initial quantity, e is the base of the natural logarithm, k is the decay constant, and t is time.
As 100 more years pass, the graph will continue its downward trend, displaying a diminishing quantity of rhodium-101. The exponential nature of decay means that the substance will continue to decrease at an ever-decreasing rate but will never reach zero. Instead, it approaches but never quite reaches a limit called the asymptote. The decay graph will continue its decline, but at a much slower pace over time.
Mathematically, the decay function doesn’t reach zero but approaches it asymptotically. This means that with each passing unit of time, the quantity of rhodium-101 diminishes, yet it will never completely disappear. In practical terms, this signifies that even after 100 more years, there will still be some remaining quantity of rhodium-101, albeit extremely small, as indicated by the approaching asymptote on the graph.
Understanding the exponential decay model helps predict the ongoing decline of rhodium-101 over the next 100 years. While the rate of decrease slows down, the substance's quantity will continue to diminish, but it will never fully deplete.