Question

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.

Answer 1

The year is 2008

Step-by-step 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).