The approximate rate of change in the number of design patent applications received in the United States in recent years is given by p′(t) = 0.01056t + 1.94, where t represents the number of years since 2000, and p represents the number of design patents (in thousands). In 2010, the number of applications for a design patent was 29,059.

(a) Find the function that gives the total number (in thousands) of design patent applications received in the U.S. in year t.
(b) Use the function from part (a) to predict the number of design patent applications in the U.S. in 2025.