The number of applications for patents, N, grew dramatically in recent years, with growth averaging about 4.6% per year. That is, Upper N prime (t )equals0.046Upper N (t ). a) Find the function that satisfies this equation. Assume that tequals0 corresponds to 1980, when approximately 117 comma 000 patent applications were received. b) Estimate the number of patent applications in 2025. c) Estimate the doubling time for Upper N (t ).

(a)

(b)885,343

(c)15 years

Step-by-step explanation:

Given that the number of applications for patents, N, grew dramatically in recentyears, with growth averaging about 4.6% per year.

Part A

The function which satisfies the equation given that that t = 0 corresponds to 1980, when approximately 117,000 patent applications were received is given by:

where:

Part B

In 2025, there are 2025 - 1980 = 45 years after 1980.

The number of patent applications 45 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 X 117,000 = 234,000

When N(t)=234000