Growth without download numbers
Apple publishes no downloads. The rating count is the public number that moves with them.
Apple does not publish downloads. The rating count does move with installs: the share of users who rate differs from app to app, but it holds for a given app, so the ratings an app gains per week is its growth line and the total is mostly its age. Compare velocity, not totals: 2,000 ratings gaining 200 a week is growing faster than 400,000 gaining 500.
A spike right after a release is the release: the update prompts the rating dialog. Read the weeks around it, not the day.
The other public movement is position: genre charts (top free, paid and grossing, read every night in the twenty largest stores) and search positions. Real downloads exist only for your own apps, through an App Store Connect key.