The use of electric vehicles will curb air pollution in the long run. The use of electric vehicles is increasing every year and estimated electric vehicles in use at any time t is given by the function V :

V(t)=‌

1

5

t3−‌

5

2

t2+25t−2
where t represents the time and t=1,2,3... corresponds to year 2001, 2002, 2003, respectively.

Based on the above information, answer the following questions :

(i) Can the above function be used to estimate number of vehicles in the year 2000 ? Justify.

(ii) Prove that the function V(t) is an increasing function.