Respuesta :
Answer:
The turtle population's rate of growth will be 32 turtles per year after 2 years and 248 per year after 6 years.
Ten years after the conservation measures are implemented the population will be 3260 turtles.
Step-by-step explanation:
To find the rate of growth of the turtle population at any time t you need to find [tex]N'(t)[/tex]
[tex]\frac{d}{dt}N(t)=\frac{d}{dt}(2t^3+3t^2-4t+1000)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\\frac{d}{dt}(2t^3)+\frac{d}{dt}(3t^2)-\frac{d}{dt}(4t)+\frac{d}{dt}(1000)\\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}\\\\N'(t)=6t^2+6t-4[/tex]
In particular, when t = 2 and t = 6, we have
[tex]N'(2)=6(2)^2+6(2)-4=32\\\\N'(6)=6(6)^2+6(6)-4=248[/tex]
so the turtle population's rate of growth will be 32 turtles per year after 2 years and 248 per year after 6 years.
The turtle population at the end of the tenth year will be
[tex]N(10)=2(10)^3+3(10)^2-4(10)+1000\\N(10)=3260 \:turtles[/tex]
