Final Answer:
The correct answer is option C: 5; 8; 11.
On a timeline, a goal that will be achieved in 5^1 years will be to the __8_^2 of one that will be achieved in _11__^3 years. A. 11; 8; 5 B. 5; 11; 8 C. 5; 8; 11 D. 8; 11; 5
Step-by-step explanation:
According to the question, the goal achieved in ^1 years should be to the ^2 of the one achieved in ^3 years. This implies that the first goal will be reached before the second goal. Among the options provided, option C (5; 8; 11) aligns with this relationship: a goal achieved in 5 years will be to the ^8 of the one achieved in 11 years.
Let's break down the comparison: if we take the first goal achieved in 5 years (^1), it is proportionally related to the second goal achieved in 11 years (^3) as 5 is to the power of 8 (5^8), as indicated by the ^8 in the second position. This corresponds to the requirement in the question that the first goal should be to the power of the second goal, and it aligns with the ratio specified.
Therefore, option C (5; 8; 11) fits the criteria provided in the question. The time differences (5, 8, 11) form a series where the earlier duration is related to the later duration according to the power specified in the question, satisfying the conditions laid out in the prompt.