Answer:
(a)

(b)885,343
(c)15 years
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:
- N(t) is the number of patent applications received at any particular year,
- t is the number of years after 1980.
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
