Answer:
Part 1: Growth Rate = 48.63%
Part 2: 3260
Step-by-step explanation:
Part1:
The number of turtles, t years from now, is found by the equation:
[tex]N(t)=2t^3 +3t^2 -4t + 1000[/tex]
Rate of growth from t=2 to t = 6:
Turtle population at end of year 2:
[tex]N(2)=2(2)^3 +3(2)^2 -4(2) + 1000\\N(2)=1020[/tex]
Turtle population at end of year 6:
[tex]N(6)=2(6)^3 +3(6)^2 -4(6) + 1000\\N(6)=1516[/tex]
Rate of Growth is:
[tex]\frac{1516-1020}{1020}=0.4863[/tex]
Growth Rate = 48.63%
Part2:
To find population after 10th year, we simply plug in 10 into the equation of N(t):
[tex]N(t)=2t^3 +3t^2 -4t + 1000\\N(10)=2(10)^3+3(10)^2-4(10)+1000\\N(10)=3260[/tex]
The population of turtles after 10th year is 3260
