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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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Answer:

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6 0
2 years ago
On a typical long distance call you talk for 30 minutes. On a typical local call you talk for 10 minutes. Your phone company off
klio [65]

The number of long distance calls to be made can be obtained by linear programming

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Reason:

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Number of minutes of calls to make each month = 240 minutes

Duration of each long distance call = 30 minutes

Duration of each local call = 10 minutes

Cost of long distance call = $0.08

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Solution:

Let <em>X</em>, represent the number of long distance calls, and let <em>Y</em> represent the number local calls

The objective function is given as follows;

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The constraints are;

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Solving we have;

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The above inequality can be plotted with MS Excel

From the objective function, P = 2.4·X + 0.3·Y, the coefficient of the long

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making the minimum possible number of long distance calls of 0, and 24

local calls will give a cost;

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Therefore, to minimize the phone bill, the number of long distance calls to

be made is <u>zero long distance calls</u>

Learn more about linear optimization here:

brainly.com/question/21491539

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MatroZZZ [7]
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Answer:

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Step-by-step explanation:

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krok68 [10]
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3 0
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