A storage system with a capacity of 10 TB currently holds 4 TB. Assume that usage grows every month by 5% of the previous month's usage (it grows like compound interest). After how many months will usage first reach 80% of capacity or more? Which of the following is the most appropriate?

Answer: B. After 15 months

80% is 8 TB, so we look for the smallest n such that 4 × 1.05ⁿ ≥ 8, that is, 1.05ⁿ ≥ 2. Since 4 × 1.05¹⁴ ≈ 7.92 TB and 4 × 1.05¹⁵ ≈ 8.32 TB, the answer is after 15 months (log 2 ÷ log 1.05 ≈ 14.2). After 8 months assumes growth of 5% of capacity (0.5 TB) every month, and after 20 months assumes a constant growth of 5% of the initial usage (0.2 TB) every month.

• A. This assumes growth of 5% of the 10 TB capacity (0.5 TB) every month.
• B. Correct. 4 × 1.05¹⁵ ≈ 8.32 TB, so usage first reaches 8 TB or more after 15 months.
• C. This assumes a constant growth of 5% of the initial 4 TB (0.2 TB) every month and ignores the compound growth.