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 2017, the number of applications for a design patent was 43,340. p'(t) = 0.01021t+2.03 Complete parts (a) and (b) below. (a) Find the function that gives the total number (in thousands) of design patent applications received in year t. (t) = Type an exact answer.)

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