Grouper Laboratories holds a valuable patent $($No$.758-6002-1$A$)$ on a precipitator that prevents certain types of air pollution.

Grouper does not manufacture or sell the products and processes it develops. Instead, it conducts research and develops products and

processes which it patents, and then assigns the patents to manufacturers on a royalty basis. Occasionally it sells a patent. The history

of Grouper patent number $758-6002-1$A is as follows.

Grouper assumed a useful life of $17$ years when it received the initial precipitator patent. On January $1,2024,$ it revised its useful life

estimate downward to $5$ remaining years. Amortization is computed for a full year if the cost is incurred prior to July $1,$ and no

amortization for the year if the cost is incurred after June $30.$ The company's year ends December $31.$

Compute the carrying value of patent No$.758-6002-1$A on each of the following dates:

a$.$ December $31,2019$$

b$.$ December $31,2023$$

c$.$ December $31,2026$$