Answer: Option E, in 12 years.
Explanation:
A geometric growth model is characterized by its finite growth rate, known as lambda. The size of the population after a unit of time has passed can be calculated using the last known size and lamba as:
Starting from the initial value of population, the next one will be calculated multiplying by 1.4, and the next one multiplying again by 1.4, thus we can define a function that relates the time passed in year to the size of the population:
Substituting our values we get the function that defines the growth of our poupulation:
Then, we just have to clear the t that gives a population of 500:
Thus, at 12 years, the population will be greater than 500.