Let P ( t ) = 26000 ( 1.04 ) t be the population of a town t years after the year 2000. Estimate in which year the population will reach 34215.

Answer 1

P(t) = 26,000 (1.04)^t

Set P(t) equal to 34,215 and solve for t. The result will be the number of years after 2000.

34,215 = 26,000 (1.04)^t

34,215 / 26,000 = (1.04)^t

log(34,215 / 26,000) = t log1.04

You should be able to solve for t and finish from here. Work with any base for the logs, as long as you use the same base. The result for t is the number of years you must add to 2000 to get to a population of 34,215.