Question

Calculate the value of intrinsic rate of natural increase for a algae population which become 2x from x in 3 years during algal bloom in a lake

Answer 1

Answer:

Answer is 69.

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Answer 2

Answer:

The value of intrinsic rate of natural growth of algae is 0.23

Explanation:

Given that,

The initial population of algae is x

$= > N_{0}=x$

The population of algae after 3 years is 2x

$= > N_{t}=2x$

The relation between initial population and population of algae after a time of t years is shown below

$N_{t}=N_{0} {e}^{rt}$

Here,

r=intrinsic rate of natural increase.

Substituting the known values,in above relation we get

$2x = x \times {e}^{3r} \\ = > 2 = {e}^{3r}$

Applying natural logarithm on both sides we get

$ln2 = 3r \: lne \\ = 2.303log2 = 3r \\ = > r = \frac{2.303 \times 0.3010}{3} = 0.23$

Therefore,The value of intrinsic rate of natural growth of algae is 0.23

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