Final answer:
The term for how much an activity can be delayed without affecting subsequent activities is called 'float' or 'slack.' In project management, this is crucial for scheduling tasks without affecting the overall project timeline.
Step-by-step explanation:
The question pertains to how much an activity can be delayed before it affects the subsequent activity. This concept is often referred to in project management and engineering as the 'float' or 'slack' time. It's the amount of time that a task in a project schedule can be delayed without causing a delay to subsequent tasks or the overall project completion date. For example, if an activity has a float of 4 days, it can be delayed by up to 4 days without impacting the start of the succeeding activity. This is an essential concept in critical path method (CPM) scheduling.
In the context provided, the delay is associated with a negative feedback system such as population growth in an ecosystem, characterized by a logistic curve. The delay (τ) needs to be smaller than the natural timescale governing the problem, which is 1/r, with r representing the rate. If the delay is longer than this natural timescale, it can cause 'overshoot,' which means that the population exceeds its sustainable level before the negative feedback corrects the growth. For instance, if the rate is 0.5, any delay over 2 years for a deer population could cause overshoot.