The temperature TnT_nTn (in ∘C{^\circ}\text{C}∘C) inside a specialized climate-controlled incubator on day n n\,n is modeled by the recurrence relation:
Tn+1=13−Tn2,n≥1 T_{n+1} = 13 - T_n^2, \quad n \ge 1 Tn+1=13−Tn2,n≥1In the case where the initial temperature is set to T1=4T_1 = 4T1=4:
(i) Calculate the value of T3T_3T3.
(ii) Deduce the value of T100T_{100}T100.
State a different value for T1T_1T1, other than T1=4T_1 = 4T1=4, which would result in the same value for T100T_{100}T100 as found in part (a)(ii). Justify your answer.
