Question

The number of homicides per 100,000 people is given by the equation

y=-0.000708x^4+0.0273x^3-0.329x^2+1.012x+12.517, where x is equal to the number of years after 1990.

A. What does this equation give as the number of homicides per 100,000 people in 2008?

B. Estimate the year after 1990 in which the number of homicides at it maximum?

C. In what year is the model not valid? Is it because the rate it positive or negative?

Answer 1

• A: 9.03
• B: 2 years
• C: 2012, negative

Explanation:

A. For x = 18, y ≈ 9.03 . . . . homicides per 100,000

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B. The curve has a maximum at about x ≈ 2.003, about 2 years after 1990.

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C. The model produces negative numbers for x > 22. It will not be valid after 2012.