Final answer:
To find the year the population broke the one million mark, we can use the formula for exponential growth. By solving the equation, the population broke the one million mark in the year 1999.
Step-by-step explanation:
To find the year the population broke the one million mark, we can use the formula for exponential growth: P(t) = P(0) * e^(kt), where P(t) is the population at time t, P(0) is the initial population, e is the base of the natural logarithm, k is the growth rate, and t is the time in years. We are given that the initial population (P(0)) is 1,145,000 and the final population (P(t)) is 1,327,000. We need to solve for the time (t) when the population reaches one million: 1,145,000 * e^(kt) = 1,000,000.
To solve for k, we can rearrange the equation: e^(kt) = 1,000,000 / 1,145,000.
Taking the natural log of both sides, we get: kt = ln(1,000,000 / 1,145,000).
Simplifying, we find: kt = -0.154.
Now we can solve for t: t = -0.154 / k.
Using the given data from the question, we have: t = -0.154 / k = -0.154 / 10 = -0.0154.
Since time cannot be negative, this implies that the population broke the one million mark before the year 2000. Therefore, to find the year, we should round up the value of t to the nearest whole number. The population broke the one million mark in the year 1999.