My hoster recently started offering Redis cache. Redis is an open source (BSD licensed), in-memory data structure store, used as a database, cache and message broker. It supports data structures such as strings, hashes, lists, sets, sorted sets with range queries, bitmaps, hyperloglogs and geospatial indexes with radius queries.
In order to improve performance, Redis works with an in-memory dataset. Depending on the use case, it can persist it either by dumping the dataset to disk every once in a while or by appending each command to a log. Persistence can be optionally disabled if you just need a feature-rich, networked, in-memory cache. Using Redis in combination with WordPress is easy using the Redis Object Cache plugin by Till Krüss.
Just make sure you follow the instructions on the Plugin page regarding the modification of the WP-Config file.
With Redis enabled, the website should now respond a lot faster. If the website continues the grow I might be implementing a CDN in the near future.