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To determine how many years it takes for a radioisotope with a half-life of one year to reduce its activity to less than 10%, we can use the concept of half-lives. The half-life is the time required for half of the radioactive substance to decay.

Initially, we start with 100% activity. After one half-life (1 year), the activity decreases to 50%. After two half-lives (2 years), the activity decreases to 25% (which is still greater than 10%). After three half-lives (3 years), the activity decreases to 12.5%, which is still above 10%. Finally, after four half-lives (4 years), the activity drops to 6.25%, which is indeed less than 10%.

Therefore, it takes four years for the radioisotope's activity to drop below 10%. This calculation illustrates the exponential decay of radioisotopes, where each subsequent half-life further reduces the remaining activity by half, demonstrating the significance of understanding half-life in the context of radioactive decay.