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The correct answer to the question is:
c. remain constant over the past 500 million years.
Explanation:
Background extinction rates have tended to remain constant over the past 500 million years. This means that, on average, the rate at which species become extinct over long periods of time has not shown a significant overall increase or decrease. While there may be fluctuations and variations within shorter time frames, the overall trend has been a relatively stable background extinction rate over the course of 500 million years.