Consider the differential equation ay′′ + by′ + cy = 0, where b2 − 4ac < 0 and the characteristic equation has complex roots λ ± iμ. substitute the functions u(t) = eλt cosμt and v(t) = eλt sinμt for y in the differential equation and thereby confirm that they are solutions.

Data from 2005 for various age groups show that for each $100 increase in the median weekly income for whites, the median weekly income of blacks increases by $105. also, for workers of ages 25 to 54 the median weekly income for whites was $676 and for blacks was $527. (a) let w represent the median weekly income for whites and b the median weekly income for blacks, and write the equation of the line that gives b as a linear function of w. b = (b) when the median weekly income for whites is $760, what does the equation in (a) predict for the median weekly income for blacks?