The number of applications for patents, n, grew dramatically in recent years, with growth averaging about 3.43.4% per year. that is, upper n prime left parenthesis t right parenthesisn′(t)equals=0.0340.034up per n left parenthesis t right parenthesisn(t). a) find the function that satisfies this equation. assume that tequals=0 corresponds to 19801980, when approximately 110 comma 000110,000 patent applications were received. b) estimate the number of patent applications in 20152015. c) estimate the doubling time for upper n left parenthesis t right parenthesisn(t).

Given that the number of applications for patents, n, grew dramatically in recent years, with growth averaging about 3.4% per year.

Part A:

The function that satisfies the equation given that that t = 0 corresponds to 1980, when approximately 110,000 patent applications were received is given by:



where, N(t) is the number of patent applications received at any particular year, t is the number of years after 1980.

Part B:

In 2015, there are 2015 - 1980 = 35 years after 1980.

The number of patent applications 35 years after 1980 is given by:



Part C:

The doubling time for N(t) is the time it takes the number of patents to be 2(110,000) = 220,000



Therefore, the doubling time for N(t) is approximately 21 years.