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14 March, 04:18

The revenue for a company is given by the function r (t) = 6t2 + 3t + 440 where t is the number of years since 1998 and r (t) is in thousands of dollars. Assuming that this trend remained the same, find the year in which this company's revenues were $1070 thousand. Round to the nearest whole year, if necessary.

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  1. 14 March, 04:23
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    The year is 2008

    Explanation:

    Acording to the formula:

    1,070 = 6t2 + 3t + 440

    0 = 6t2 + 3t + 440 - 1,070

    0 = 6t2 + 3t - 630

    This is a quadratic function and we must solve the roots.

    x = (-b±√ (b^2-4ac)) / 2a

    Where:

    x = t (number of years since 1998)

    a = 6

    b = 3

    c = - 630

    t = (-3±√ (3^2-4*6 * (-630))) / (2*6)

    t1 = 10

    t2 = - 10.5

    Since a negative value is illogical, we take the positive root (t = 10). So the result is the year 2008 (1998 + 10 years).
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