Hello everyone.

My task is to build a growth model for a company. The company offers services to businesses - and thus allowing the businesses to recruit new clients.
Assumptions:
- I started working with 10 businesses
- A business I start working with initially has 20 clients
- I'm recruiting 3 new businesses every month
- A businesses which is using my services will get 5 new client after every month of service (if he started getting my service on July 1st then on August 1st he will have 5 new clients)

I need to build a formula to calculate how much clients and how much businesses there will be in 6 months.

Here is how I started calculating manually:

MONTH 1:
10 (type A) businesses
20 clients (per business)
TOTAL - 10 businesses
TOTAL - 200 clients

MONTH 2:
10 (type A)businesses
25 clients (per business)
3 (type B) businesses
20 clients (per business)
TOTAL - 13 businesses
TOTAL - 310 clients

MONTH 3:
10 (type A)businesses
30 clients (per business)
3 (type B)businesses
25 clients (per business)
3 (type C) businesses
20 clients (per business)
TOTAL - 16 businesses
TOTAL - 435 clients

etc...

I need these to be variables that can be changed:
- number of businesses I started with
- how much new businesses I find every month
- how much new clients a businesses recruits after working a month with me
- how much clients a businesses initially has

To build a formula for calculating the number of clients and businesses after a certain number of months, you can use variables and arithmetic operations. Here's how you can approach it:

1. Define the initial values:
- Number of businesses you started with (let's call it "initial_businesses"): 10
- Number of clients a business initially has (let's call it "initial_clients"): 20

2. Define the growth rates and variables:
- Number of new businesses recruited every month (let's call it "new_businesses_per_month"): 3
- Number of new clients a businesses recruits after each month of service (let's call it "new_clients_per_month"): 5

3. Calculate the number of businesses and clients for each month:

For month 1:
- Number of businesses: initial_businesses
- Number of clients: initial_businesses * initial_clients

For month 2:
- Number of businesses: initial_businesses + new_businesses_per_month
- Number of clients: (initial_businesses * initial_clients) + (new_businesses_per_month * initial_clients)

For subsequent months:
- Number of businesses: previous_number_of_businesses + new_businesses_per_month
- Number of clients: (previous_number_of_businesses * initial_clients) + (new_businesses_per_month * initial_clients) + (new_clients_per_month * previous_number_of_businesses)

You can apply this calculation for each month, updating the values with each iteration.

To calculate the number of businesses and clients after 6 months, you can use a loop or directly calculate the values for each month individually.