Answer
[1, t]
average rate of change = $t+1$
the instantaneous rate of change at t = 1 equal $2$
[2, t]
average rate of change = $t+2$
the instantaneous rate of change at t = 2 equal $4$
Work Step by Step
[1, t]
average rate of change = $\frac{Q(t)-Q(1)}{t-1}$ = $\frac{t^{2}-1}{t-1}$ = $\frac{(t-1)(t+1)}{t-1}$ = $t+1$
the instantaneous rate of change at t = 1 equal to $t+1$ = $1+1$ = $2$
[2, t]
average rate of change = $\frac{Q(t)-Q(2)}{t-2}$ = $\frac{t^{2}-4}{t-2}$ = $\frac{(t-2)(t+2)}{t-2}$ = $t+2$
the instantaneous rate of change at t = 2 equal to $t+2$ = $2+2$ = $4$
