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 (d)/(dx)3t^2-12t+4`

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

`\\ \sf\longmapsto (d)/(dx)3t^2-(d)/(dx)12t+(d)/(dx)40`

`\\ \sf\longmapsto 6t-12`

Now

• t=8..

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

`\\ \sf\longmapsto 48-12`

`\\ \sf\longmapsto 36`