Given that the grant increases by 5% each year, this forms a geometric progression (GP) with the first term, \(a = 5000\), and common ratio, \(r = 1.05\).

(i) To find the grant given in 2011, we calculate the 11th term of the GP:

\(a r^{n-1} = 5000 \times 1.05^{10}\)

\(= 5000 \times 1.62889 \approx 8144\)

(ii) To find the total amount given from 2001 to 2011, we use the sum formula for a GP:

\(S_n = a \frac{r^n - 1}{r - 1}\)

\(S_{11} = 5000 \frac{1.05^{11} - 1}{1.05 - 1}\)

\(= 5000 \frac{1.71034 - 1}{0.05}\)

\(= 5000 \times 14.2068 \approx 71034\)