Question

Biologists estimate that the number of animal species of a certain body length is inversely proportional to the square of the body length.1 Write a formula for the number of animal species, N, of a certain body length as a function of the length, L. Use k as the constant of proportionality.

Answer 1

Answer:

$N(L)=\frac{k}{L^2}$

Step-by-step explanation:

Here, N represents the number of animal species and L represents a certain body length,

According to the question,

$N\propto \frac{1}{L^2}$

$\implies N=\frac{k}{L^2}$

Where, k is the constant of proportionality,

Since, with increasing the value of L the value of N is decreasing,

So, we can say that, N is dependent on L, or we can write N(L) in the place of N,

Hence, the required function formula is,

$N(L)=\frac{k}{L^2}$