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xeze [42]
3 years ago
10

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
Mathematics
1 answer:
bulgar [2K]3 years ago
3 0

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

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<u>Answer:</u>

So all the possible solutions are:

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<u>Solution Steps:</u>

<em>First you need to solve the real inequality to understand how to find the rest of the possible equations. </em>

<u>Add 78 to both sides:</u>

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<em>So now we know the real answer, but it ask for all possible answers. </em>

(Means anything larger than 300 when you plug it into x - 78 > 300.)

<u>Numbers that are greater than 378:</u>

  1.)  377-78=299 > 300  (False)

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  5.)  400-78=322>300  (True)

  6.)  379-78=301>300  (True)

  7.)  222-78=144>300  (False)

  8.)  378.6-78=300.6>300 (True)

______________________________

 \bold{Hope~this~helps!}\\\bold{If~you~need~help~with~anything~else,~feel~free~to~ask!}\\\\\bold{~~~~~-TotallyNotTrillex}

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