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.

Question

Business

Cayden Parrish

1 April, 22:55

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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Eliezer Watts · Answer 1

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).