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The following equation allows us to make projections on the sale of iPhones:

\[ Y = 39.3 + 22.7x + 5.07x^2 \]

For what year was the sale of 440 iPhones projected, if the average is 1996?

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Answer :

Final answer:

The sale of 440 iPhones was projected for the year 2012 according to the given equation.

Explanation:

To find the year for which the sale of 440 iPhones was projected, we can substitute Y = 440 into the equation Y = 39.3 + 22.7x + 5.07x² and solve for x. The equation becomes 440 = 39.3 + 22.7x + 5.07x².

Rearranging this quadratic equation, we get 5.07x² + 22.7x - 400.7 = 0. Using the quadratic formula, we find two possible values for x, representing different years. However, since the average year is specified as 1996, we choose the year that is closer to 1996.

The two solutions for x are approximately -15.95 and 15.77. Since a negative year is not meaningful in this context, we discard the negative solution. Therefore, the positive solution of x ≈ 15.77 corresponds to the year 1980.

Adding this to the average year of 1996 gives us the projected year for the sale of 440 iPhones: 1996 + 15.77 ≈ 2011.77. Rounding to the nearest whole year, the sale of 440 iPhones was projected for the year 2012.

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