The problem I'm worried about is precisely what you're warning against: I'm confident that I can successfully launch in one city (with my own funds) but I'm afraid that this will be considered post-launch and pre-traction when I solicit investors.
if you can recoup your funds 10 days after launching in one such city, why are you worried about the investors?
launch in 1 city -> recoup -> launch in another city -> recoup -> ... do that enough times and you either have traction and/or you don't really need investors.
i suspect that your prediction of the recoup-ability is what's off.
The startup's customers are from among many verticals. Acquiring those customers is why I need the sales team. I can work to acquire a few myself within a specific vertical. To service the acquired customers is where the monetary expense is required (think PPC ads that are later billed to the customers, for example).
Of course, I can do one at a time, but why? That's the point of me wanting to seek funding - to scale quickly...to go after multiple companies in multiple cities within multiple industries.
The dynamic you are describing captures probably the majority of all the pitches investors hear. Everyone thinks they can "recoup" within X days of spending on sales, marketing, and support. The reason to do it one city at a time is that it allows you to demonstrate two things: (a) that your model actually does work, unlike the 1000 competing pitches that claim the same thing but don't work at all, and (b) that you don't actually need their investment, which gives you leverage in your negotiation and, counterintuitively, makes you a more attractive investment.
It assigns a sentiment score based on a large bag of words. I'm making improvements to it each day, and it's slowly getting better. Terrible at picking up sarcasm though, but I think most sentiment analysis tools are.
I just have a website. It's almost all word-of-mouth, blog posts, and people posting on forums recommending it that drives traffic. I do some Google Ads.
It's a one-time sale. It's a freemium model. You can download the app and get limited functionality. You can purchase for $10 the "Pro" version which is a serial number that unlocks the advanced features.
For a while I was doing cheaper time-limited licenses, like $1 for 6 months, $2 for 1 year, etc and $10 for lifetime.
Best source of customers is from free users. I started the app as free until version 3.0 when I switched to freemium. Sales have been fairly consistent each month for years, with spikes when a blog picks it up.
Probably manga. The US manga market has expanded hugely since I started reading manga (~8 years ago). Just about any genre (or subject matter) you can name has manga dedicated to it, which contributes to its ability to appeal across all age groups.
The other big thing is that most of the hardcore fans (those who would also like to read on their iOS devices) like to download & read scanlations (A $10 manga volume takes at most 90 minutes to read, so this is an expensive hobby for a hardcore fan, many of whom are children. Also, the hardcore fans prefer the scanlations because they allow them access to manga that hasn't been released in America or has been Americanized by the official English-language translator/publisher.), which are easily placed on an iPhone/iPad, whereas American comics would much more often require legal licensing.
