Question

A certain species of turtle faces extinction because dealers collect truckloads of turtle eggs to be sold as aphrodisiacs. After severe conservations measures are implemented, it is hoped that the turtle population will grow according to the rule N(t)=2t^3+3t^2-5t+1,000 (0 ≤ t ≤ 10), Where N(t) denotes the population at the end of year t. A) Find the rate of growth of the turtle population when t=2 __________ turtles/yr. B) Find the rate of growth of the turtle population when t=8 __________ turtles/yr. C) What will be the population 10 years after the conservation measures are implemented? __________ turtles

Answer 1

Given that

N(t)=2t³+3t²-5t+1000

By differentiating with respect to t

`(dN)/(dt)=6t^2+6t-5`

a)

At t= 2 year

`(dN)/(dt)=6t^2+6t-5`

`(dN)/(dt)=6* 2^2+6* 2-5`

`(dN)/(dt)=31\ turtles/yr`

b)

at t= 8 yr

`(dN)/(dt)=6t^2+6t-5`

`(dN)/(dt)=6* 8^2+6* 8-5`

`(dN)/(dt)=427\ turtles/yr`

c)

At t= 10 year

N(t)=2t³+3t²-5t+1000

N(t)=2 x 8³+3 x 8²-5 x 8+1000

N(t)=2,176 turtles