please show calculation

Question 7 (1 Point) Qui Mike is a taxi driver. He needs to decide how often (i.e., every how many days) he should replace his taxi. Without the consideration of time value of money, the price of a new taxi is $10000. As a taxi is ordered, there is a usage cost for Mike (i.e., the daily cost of fuel consumption of taxi is relatively small at the beginning, but with the increase of service time, the daily cost of fuel consumption becomes larger). A new taxi is purchased at the beginning of day 1, and there is a usage cost of $100 in day 1, $102 in day 2, $104 in day 3, etc. When a new taxi is purchased, the daily usage costs will be $100, $102, $104, ... again, and the older taxi has a salvage value of $200 (note that this means actually there is a salvage cost of $200 for disposing of a taxi). Assume that the taxi replacement decision will be repeated forever. What is the optimal number of days after which he should replace his taxi? (Please show your calculation.) a