Pharoah Inc. purchased a patent on January $1,2023$ for $$460000.$ Pharoah did not record amortization expense on the patent for $2023$ and $2024.$ At the purchase date, the expected useful life of the patent was $10$ years. At December $31,2025,$ what should be recorded as the amortization expense?

$$92000$

$$46000$

$$0$ because the value of the patent has not decreased

$$138000$