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Scientists are monitoring the populations of two insect species in a remote location in Alabama. They estimate that the current population of insect A is 2.5 million. But it’s declining at the rate of 4% per year because of habitat loss. The estimated population of insect B is 1.2 million, and it’s increasing at the rate of 200,000 per year. Let x represent the population of each insect species in millions, and y represent the elapsed time in years. Which equation can be used to determine how long it will take for the populations of the two species to be equal? 2.5e-0.04x = 1.2 + e0.2x 2.5e0.04x = 1.2 + 0.2x 2.5e-0.04x = 1.2 + 0.2x 2.5 + 0.04x = 1.2 + 0.2x

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Answer:

2.5e-0.04x = 1.2 + 0.2x

Step-by-step explanation:

Given that:

Insect A:

Initial population, Po = 2.5 million

Rate of decline = 4%

Insect B:

Initial Population (Po) = 1.2 million

Yearly increase = 200,000 = (200,000/1,000,000) = 0.2

For insect A:

P(t) = Po(1 - r)^t = Po*e^-rt

Po*e^-rt = 2.5e^-0.04t ----(1)

For Insect B:

P(t) = Po + (yearly increase) * t

P(t) = 1.2 + 0.2t - - - - - (2)

Equating (1) and (2)

2.5e^-0.04t = 1.2 + 0.2t