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?

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.