1. **State the problem:** Jason records songs in a pattern: 2 songs on day 1, 4 songs on day 2, 8 songs on day 3. We need to find how many songs he records on day 5. 2. **Identify the pattern:** The number of songs doubles each day. This is a geometric sequence where each term is multiplied by 2. 3. **General formula for the pattern:** The number of songs on day $n$ is given by $$a_n = 2^n$$ where $n$ is the day number. 4. **Calculate for day 5:** Substitute $n=5$ into the formula: $$a_5 = 2^5$$ 5. **Evaluate:** $$2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$$ 6. **Answer choice:** The correct answer is C: $2^5$ songs, which equals 32 songs. Therefore, Jason records 32 songs on day 5.