During a recent period of time, the numbers (in thousands) of makes M and females F that attend colleges and other degree programs in the United States can be modeled by M=19.7t^2+310.5t+7539.6 and F=28t^2+368t+10127.8 where tis time in years. Write a polynomial that represents the total number of people Pattending colleges and other degree programs. P=18,395.6t^3 P=47.7t^2+678.5t+17,667.4 P=47.7t^4+678.5t^2+17,667.4 P=-8.3t^2-57.5t-2588.2

To find the polynomial that represents the total number of people P attending colleges and other degree programs, we need to add the given polynomials for males M and females F.<br /><br />Given:<br />$M = 19.7t^2 + 310.5t + 7539.6$<br />$F = 28t^2 + 368t + 10127.8$<br /><br />To find P, we add M and F:<br />$P = M + F$<br />$P = (19.7t^2 + 310.5t + 7539.6) + (28t^2 + 368t + 10127.8)$<br /><br />Combining like terms:<br />$P = 19.7t^2 + 28t^2 + 310.5t + 368t + 7539.6 + 10127.8$<br />$P = 47.7t^2 + 678.5t + 17567.4$<br /><br />Therefore, the polynomial that represents the total number of people P attending colleges and other degree programs is:<br />$P = 47.7t^2 + 678.5t + 17567.4$