A small business backs up its data daily to a cloud service. On day\,1 the backup file is 0.5\,GB and each subsequent day's backup is 10\% larger than the previous day (i.e., the sizes form a geometric progression with ratio 1.10). The business retains the last 30 days of backups; older files are deleted. The service charges $\$0.02$ per GB transferred (upload only) and $\$0.05$ per GB stored per month. (a) Compute the total monthly cost (transfer + storage) for a 30‑day month. (b) If the business compresses each backup to 70\% of its original size before uploading, what are the new total monthly cost and the percentage saving compared with part\,(a)? Give costs to two decimal places and the saving as a percentage to the nearest whole number.

Question

A small business backs up its data daily to a cloud service. On day\,1 the backup file is 0.5\,GB and each subsequent day's backup is 10\% larger than the previous day (i.e., the sizes form a geometric progression with ratio 1.10). The business retains the last 30 days of backups; older files are deleted. The service charges $\$0.02$ per GB transferred (upload only) and $\$0.05$ per GB stored per month.   (a) Compute the total monthly cost (transfer + storage) for a 30‑day month.   (b) If the business compresses each backup to 70\% of its original size before uploading, what are the new total monthly cost and the percentage saving compared with part\,(a)? Give costs to two decimal places and the saving as a percentage to the nearest whole number.

Accepted Answer

Total cost without compression: $2.91; with 30% compression: $2.03; saving ≈30%

Neco 2024 Data Processing Question 35

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