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.

the oceanic zone is typically defined as the area of the ocean lying beyond the continental shelf, but operationally is often referred to as beginning where the water depths drop to below 100 meters (328 feet), seaward from the coast to the open ocean.

explanation: