The model is for the city to city expansion of a software as a service (SAAS) like Uber and the challenge is as follows:
When first expanding to a city, in month 1 the market penetration of the product would be say 0.5% and month on month the market penetration would increase by 5% until a maximum of 80%.
Simultaneously, the SAAS is delivered to a new city every month, so in month 2, the market penetration in city 1 would be 5.5% and the market penetration in city 2 would be 0.5%.
The simple way to model would be to form 2 rows, row 1 being the number of cities, and row 2 being the market penetration % and row 3 being the multiplication of the 2, however this falsely assumes that with every city you expand to, the market penetration begins at the penetration rate of the 1st city.
Other than listing out the market penetration for every city, line by line, is there a simplier way to model this?