k$)$ The relation between strength $(MPa)$ and maturity $(C.hr)$ for a concrete mix is as follows:

$F_C=-33+24logM$

If the concrete will be cured using an atmospheric pressure steam curing cycle as$.$ shown in the figure below. Calculate the strength at the end of the steam curing cycle. If the strength required at the end of the steam curing cycle is $40$MPa, what would be the time needed for the maximum temperature period to achieve this strength? $(7$ marks$)$