Using a geometric growth model to predict population growth, a population of 10 individuals at time zero with a finite growth rate (x? , lambda? , lambda) of 1.4 would be expected to exceed 500 in how many years?
a. 7
b. cannot calculate from the information given
c. 10
d. 16
e. 12
f. 21

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.

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