Question

The population of a city of 100 people increases at an intrinsic rate of 0.1,but the city has accesses to food and housing for only 200 people what will the current growth rate of the population be?

Answer 1

Answer:

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Answer 2

The current growth rate of the population will be 5.

Given,

The total population of the city= 100

Value of intrinsic rate= 0.1

Number of people for housing (k)= 200

To Find,

Current growth rate of the population

Solution,

The intrinsic growth rate = $\frac{dN}{dT} = rN$

where r= 0.1 and N= total population =100

therefore, the value of rN = 100*0.1

Now, $\frac{dN}{dT} = \frac{rN(k-N)}{k}$

⇒ $\frac{dN}{dT} = \frac{0.1*100(200-100)}{200}$

⇒ $\frac{dN}{dT} = 5$

Hence, the current growth rate of the population will be 5.

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