Final answer:
Organism 1 reached its population peak after transition from exponential to logistic growth, with a carrying capacity of 120 individuals. Assuming a 53-year delay in recognizing organism 2's extinction, organism 1 likely reached its peak after this period. However, this is an estimate and specific data on the populations' dynamics would be needed for precise timing.
Step-by-step explanation:
When considering the population growth patterns and extinctions, we can infer that organism 1 reached its highest population level after a period of exponential growth was followed by a logistic phase. Based on the exponential growth model, a population grows rapidly when resources are abundant but slows as resources become depleted and stabilizes at the carrying capacity. This carrying capacity, for organism 1, was 120 individuals. If organism 2 went extinct, this could have led to a release of resources or lessen competition, allowing organism 1 to grow until it hit its carrying capacity. Given that extinctions can go unnoticed for an average lag of 53 years, and assuming this holds true here, we might say that the population of organism 1 peaked sometime after this 53-year lag period.
However, to precisely determine how long it took for the population of organism 1 to reach its highest point after the extinction of organism 2, we would need more specific data on the interaction between these two populations and the timing of the extinction event. Nonetheless, the information provided suggests a delayed recognition of extinction events and the possibility that organism 1's population might peak only after such recognition, implying a period longer than 53 years following the disappearance of organism 2.