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The function P(t) represents the population P, in millions, of a certain city t years after 2000. Which statement interprets P(10) = 8?

Rationale

The population was 8 million in 2010.

P(10) = 8 indicates that 10 years after the year 2000, which is 2010, the population of the city is 8 million. This explicitly defines the population at that specific point in time.

A (The population increases by 10 million every 8 years.) YOUR ANSWER

This statement incorrectly interprets the function P(t). P(10) = 8 does not provide information about the rate of population increase; rather, it specifies the population size at a particular time, not a growth rate.

B (The population increases by 8 million every 10 years.) YOUR ANSWER

Similar to choice A, this option misinterprets the function. While it mentions a growth amount, P(10) = 8 solely tells us the population at a specific year rather than any details about the rate of increase over a decade.

C (The population was 10 million in 2008.) YOUR ANSWER

This statement is inaccurate because P(10) refers to the year 2010, not 2008. Therefore, it does not reflect the population in 2008, which is two years before the time referenced by P(10).

D (The population was 8 million in 2010.) CORRECT

This choice accurately reflects the information given by the function P(t). Since P(10) = 8 corresponds to 10 years after 2000 (which is 2010), it clearly states that the population at that time is 8 million.

Conclusion

The interpretation of P(10) = 8 is straightforward: it indicates the population of the city is 8 million in the year 2010. The other options either misinterpret the function or provide incorrect information about the population at different years, emphasizing the importance of accurately analyzing function values in context.

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