$(45$ pts$.)$ The population data for the cities of Chicago and Houston are as follows:

a$.(20$ pts$.)$ Estimate the population of both Chicago and Houston in the year $2030$

and $2050$ using both geometric and arithmetic methods of population forecasting.

b$.(20$ pts$.)$ Considering an additional factor that may influence population growth,

calculate the population for Houston in the year $2050$ and $2080.$

Immigration Factor: Assume that Houston will experience a significant increase

in immigration due to favorable immigration policies and economic opportunities.

This will result in an additional $100,000$ people migrating to Houston annually

from $2030$ onwards.