Final answer:
To estimate the year when the population reaches 9005, we solve the equation 9005 = 6000(1.07)^t, arriving at the year 2006 after rounding up the solution t ≈ 6.01.
Step-by-step explanation:
To estimate in which year the population of a town will reach 9005, given a population growth function P(t) = 6000(1.07)t where t is the number of years after the year 2000, we must solve the equation 9005 = 6000(1.07)t for t.
First, we divide both sides by 6000 to isolate the exponential term, resulting in 1.5008333 = (1.07)t. Taking the natural logarithm of both sides gives us ln(1.5008333) = t * ln(1.07).
To find t, we then divide ln(1.5008333) by ln(1.07), resulting in t ≈ 6.01. Since we cannot have a fraction of a year and we should round up to ensure the population exceeds 9005, the town is expected to reach a population of 9005 in the year 2006.