Answer:
After 2009 the quality of the forests in this country improving.
Step-by-step explanation:
Consider the provided function.
![f(t) = \frac{1}{3}t^3-\frac{5}{2}t^2 + 80](https://tex.z-dn.net/?f=f%28t%29%20%3D%20%5Cfrac%7B1%7D%7B3%7Dt%5E3-%5Cfrac%7B5%7D%7B2%7Dt%5E2%20%2B%2080)
![f'(t) = t^2-5t](https://tex.z-dn.net/?f=f%27%28t%29%20%3D%20t%5E2-5t)
Substitute f'(t)=0.
![t^2-5t=0](https://tex.z-dn.net/?f=t%5E2-5t%3D0)
![t(t-5)=0](https://tex.z-dn.net/?f=t%28t-5%29%3D0)
![t=0\ or\ t=5](https://tex.z-dn.net/?f=t%3D0%5C%20or%5C%20t%3D5)
It is given that (0 ≤ t ≤ 10)
The test interval are (0,5) and (5,10)
For (0 < t < 5) the value of
For (5 < t < 10) the value of
Hence, the function is increasing from (5,10).
t = 0 corresponds to 2004.
Therefore, after 2009 the quality of the forests in this country improving.