Question

The population of a species of starfish in the Gulf of Mexico is decreasing at an exponential rate, A(t) = A0e(kt) . Five years ago the population was 10,000. The current population is only 2000. When the population is 500, the starfish population cannot recover. When will this event occur?

Answer 1

Linearization of the given exponential equation gives us,
                            lnA(t) = lnAo + kt
Using the current population of 2000 and the population 5 years ago which was 10,000, we solve for the value of k,
                                ln 2000 = ln 10,000 + k(5)
The value of k is -0.321887

Using this value,
                           ln(500) = ln (2,000) + (-0.321887)(t)
The value of t is equal to 4.306 years. Therefore, the starfish will be considered endangered as of 2022.