Final answer:
The population at the beginning of 2019 is estimated to be about 4823 people. It will take approximately 71.3 years for the population to reach 9000. The population will reach 9000 in the year 2066.
Step-by-step explanation:
To estimate the population at the beginning of the year 2019, we can use the exponential growth formula: P(t) = P0 * e^(rt), where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and e is the constant approximately equal to 2.71828.
From the information given, we know that the initial population in 1995 was 3306 and the population in 2014 was 4657. To find the growth rate, we can use the formula: r = ln(P2/P1) / (t2 - t1), where P1 is the initial population, P2 is the final population, t1 is the initial time, and t2 is the final time. Plugging in the values, we have r = ln(4657/3306) / (2014-1995).
By calculating this value, we find that r is approximately 0.024. Now, we can substitute the values into the exponential growth formula with t=2019 (rounding the value to the nearest person): P(2019) = 3306 * e^(0.024 * (2019-1995)). Solving this equation, the estimated population at the beginning of 2019 is about 4823 people.
To find how long it will take for the population to reach 9000, we can rearrange the exponential growth formula to solve for time: t = (ln(P/P0)) / r, where P is the desired population. Plugging in the values, we have t = (ln(9000/3306)) / 0.024. Calculating this value, we find that it will take approximately 71.3 years for the population to reach 9000, rounding to 2 decimal places.
Finally, to find the year when the population reaches 9000, we can add the calculated time to the initial year: 1995 + 71.3 = 2066. Therefore, the population will reach 9000 in the year 2066.