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max2010maxim [7]
2 years ago
13

A city block has 6 pigeons and then 1 week later there are 9 pigeons. Let P(t)be the number of pigeons where t is measured in we

eks.
Assuming the growth continues proportionally, at the same rate, what is the differential equation which describes the growth of the pigeon population?
Mathematics
1 answer:
Pavel [41]2 years ago
8 0

Using proportions, it is found that the differential equation which describes the growth of the pigeon population is given by:

\frac{dP}{dt} = 1.5P

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, considering the initial population and the population one week later, the rate of growth is given by:

k = 9/6 = 1.5.

The standard differential equation for population growth is:

\frac{dP}{dt} = kP

Hence:

\frac{dP}{dt} = 1.5P

More can be learned about proportions at brainly.com/question/24372153

#SPJ1

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An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15. 7 inches, so the equ
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The lengths that make the sense for the value of b are 0.5 inches and 2 inches.

<h2>Given </h2>

An isosceles triangle has two sides of equal length, a, and a base, b.

The perimeter of the triangle is 15.7 inches, so the equation to solve is 2a + b = 15.7.

<h3>What is the triangle inequality theorem?</h3>

If two sides of a triangle are unequal, the longer side has a greater angle opposite to it.

\rm a+a > b\\\\2a > b

The equation of the perimeter of the triangle;

\rm 2a+b = 15.7\\\\2a = 15.7-b\\\\a = \dfrac{15.7-b}{2}

1. Substitute b = 0.5 in the equation;

\rm a = \dfrac{15.7-b}{2}\\\\  a = \dfrac{15.7-0.5}{2} \\\\ a = \dfrac{15.2}{2}\\\\a = 7.6

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Verify the triangle inequality theorem;

0.5 + 7.6 > 7.6 is true

7.6 + 7.6 > 0.5 is true

2. Substitute b = 2 in the equation;

\rm a = \dfrac{15.7-b}{2}\\\\  a = \dfrac{15.7-02}{2} \\\\ a = \dfrac{13.7}{2}\\\\a = 6.85

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Verify the triangle inequality theorem;

0.5 + 76.85 > 6.85 is true

6.85 + 6.85 > 2 is true

Hence, the lengths that make the sense for the value of b are 0.5 inches and 2 inches.

To know more about the Triangle inequality theorem click the link given below.

brainly.com/question/1026055

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