Two different hot objects, A and B$,$ both at $100\mathrm{.}0$C$,$ are placed in a room at $20\mathrm{.}0$C$.$ After $20\mathrm{.}0$ minutes, A has cooled down to $70\mathrm{.}0$C and B to $80\mathrm{.}0$C$.$

$($a$)$ Which one has the greater decay constant?

$($b$)$ What is the ratio of the larger decay constant to the smaller?

$($c$)$ How long will it take A to cool down from $70\mathrm{.}0$ to $40\mathrm{.}0?$

$($d$)$ How long for A to cool down from$40\mathrm{.}0$to$20\mathrm{.}0?$