The approximate rate of change in the number of design patent applications received in recent years is given by the equation below, where t represents the number of years since 2000 and p represents the number of design patents [in thousands}. In 2012, the number of applications for a design patent was 32,799. p'(t) = D.D1076t+1.91 Complete parts (a) and (b) below. E) {a} Find the function that gives the total number {in thousands) of design patent applications received in year L pm = E {Type an exact answer.) {bl Use the function from part (a) to predict the number of design patent applications in 2024. 3 {Round to the nearest whole number as needed.)