Question

The rate of growth of the population of rabbits in China is proportional to the current rabbit population. The population after t years is R(t). Write the differential equation for which R(t) is a solution. Your equation should involve an unknown constant

Initially, there are 100 rabbits but the population is increasing at a rate of 20 per year. Use this information to find the unknown constant in part That is, write the differential equation (without an unknown constant) for which R(t) is a solution

Find the population of rabbits in year t. That is, find R(t

Find the time t in which there are 1, 000 rabbits

Answer 1

Let R(t) denote the current rabbit population after t years.

Then dR/dt denotes the rate of growth of the population of rabbits.

where k is the constant of proportionality(unknown constant)

a) Given when R=100 rabbits ,dR/dt=20

  

  

b) To find the differential equation.

..

EQUATION USED

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Integrating both sides,

...Where C is a constant of Integration

Taking ani logarithm on both sides

EQUATION USED

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   ...................

• It is given Initially(means t=0) , population is 100 rabbits(R=100)

   ........

C)

When R=1000,t=?

Taking logarithm on both sides,

EQUATION USED

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Therefore in 5 years , population will be 1000.