3 years ago

Step by step explanation

Mathematics

1 answer:

Liono4ka [1.6K]3 years ago

7 0

Answer:

x/5 + 2 = 4

Step-by-step explanation:

x/5 + 2 = 4

x/5 = 2

x = 10

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The population of a certain species of insect is given by a differentiable function P, where P(t) is the number of insects in th

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Answer:

$\frac{dP}{dt} \ =\ \frac{1}{5}P$

Step-by-step explanation:

Given

Variation: Directly Proportional

Insects = 10 million when Rate = 2 million

i.e. $P = 10\ million$ when $\frac{dP}{dt} = 2\ million$

Required

Determine the differential equation for the scenario

The variation can be represented as:

$\frac{dP}{dt} \ \alpha\ P$

Which means that the rate at which the insects increase with time is directly proportional to the number of insects

Convert to equation

$\frac{dP}{dt} \ =\ k * P$

$\frac{dP}{dt} \ =\ kP$

Substitute values for $\frac{dP}{dt}$ and P

$2\ million = k * 10\ million$

Make k the subject

$k = \frac{2\ million}{10\ million}$

$k = \frac{2}{10}$

$k = \frac{1}{5}$

Substitute $\frac{1}{5}$ for k in $\frac{dP}{dt} \ =\ k * P$

$\frac{dP}{dt} \ =\ \frac{1}{5}* P$

$\frac{dP}{dt} \ =\ \frac{1}{5}P$

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