The population, in millions, of a city t years after 2000 is given by the function P(t) = 2.9 - 0.008t.
Which statement is true?
A. The population is increasing by 8,000 people per year.
B. The population is decreasing by 8,000 people per year.
C. They were 8,000 people living in the city in 2000.
D. In ten years, there will be 8,000 people living in the city.
To determine which statement is true, we need to analyze the given population function P(t) = 2.9 - 0.008t.
A. The statement "The population is increasing by 8,000 people per year" is not true. To see how the population is changing over time, we need to consider the coefficient of t, which is -0.008. Since it is negative, it indicates a decrease in population over time, not an increase.
B. The statement "The population is decreasing by 8,000 people per year" is true. The coefficient of t, which is -0.008, represents the decrease in population per year. Specifically, the population decreases by 0.008 million (or 8,000) people per year.
C. The statement "There were 8,000 people living in the city in 2000" is not true. To find the initial population in 2000, we need to substitute t = 0 into the function. P(0) = 2.9 - 0.008(0) = 2.9. Therefore, there were 2.9 million people in the city in 2000, not 8,000.
D. The statement "In ten years, there will be 8,000 people living in the city" is not true. To find the population in ten years, we substitute t = 10 into the function. P(10) = 2.9 - 0.008(10) = 2.9 - 0.08 = 2.82. Therefore, in ten years, there will be 2.82 million people living in the city, not 8,000.
Based on the analysis, the correct answer is B. The population is decreasing by 8,000 people per year.