Question

A population of rabbits at time t increases at a rate of 40-12t+3t^2 rabbits per year where t is measured in years. Find the population after eight years if there are 10 rabbits at t=0?

Answer 1

We have to find derivative of t

$\\ \sf\longmapsto \dfrac{d}{dx}3t^2-12t+4$

$\boxed{\sf \dfrac{d(x^n)}{dx}=nx^{n-1}}$

$\\ \sf\longmapsto \dfrac{d}{dx}3t^2-\dfrac{d}{dx}12t+\dfrac{d}{dx}40$

$\\ \sf\longmapsto 6t-12$

Now

• t=8..

$\\ \sf\longmapsto 6(8)-12$

$\\ \sf\longmapsto 48-12$

$\\ \sf\longmapsto 36$