The population of a town at a rate of $3 per year. in 2005 there were 1600 people. find the population in 2006

Are you sure it's $3 per year? Perhaps you meant that the town's population grew at the rate of 3% per year.

If that's the case, then P = 1600*(1.03)^t where t is the number of years that have elapsed.

Then, in 2006, 1 year later, the population is P = 1600*(1.03*1), or 1648.