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Answer :
Final answer:
The technology metric doubles every 15 months starting from the base year. To improve 1024x from the base year, it will take 84 months.
Explanation:
The technology metric doubles every 15 months starting from the base year. To find how long it will take to improve 1024x from the base year, we can use the rule of 70. According to the rule, the doubling time associated with a percentage growth rate is 70 divided by the percentage rate.
In this case, we are doubling the metric so the growth rate is 100%. Therefore, the doubling time is 70/100 = 0.7 years or approximately 0.7 * 12 = 8.4 months.
Since we want to improve it 1024x, we need to double it 10 times (2^10 = 1024). Therefore, the total time required is 10 * 8.4 months = 84 months.
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