Question

In 2005, Capital City determined its population could be expressed by the function P(x) = -15x + 53,708 where x is the number of years. Which of the following statements is true?

A. The city's population was 53,703 in 2005.


B. The city's population was 53,813 in 2011.


C. The city's population is increasing at a rate of 15 people each year.


D. The city's population is decreasing at a rate of 15 people each year.

Answer 1

D. The city's population is decreasing at a rate of 15 people each year.

Explanation:

We presume x=0 in 2005, so the population in 2005 is ...

P(0) = -15·0 +53,708 = 53,708 . . . . . . not 53,703

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In 2011, the population would correspond to that for x=6, so would be ...

P(6) = -15·6 +53,708 = 53,618 . . . . . . not 53,813

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The x-coefficient of -15 means that when x increases by 1, the population decreases by 15. The population decreases by 15 each year, not increases.