a) By inspecting and comparing the graphs, both of them tend to decrease sharply at the beginning, and the rate of decrease declines as it eventually levels off to some value. In other words, both graphs appear exponential having an asymptote.

b) At the start of the experiment, Time $=0$, and from the graph, the corresponding temperature is $85^circ$ C

c) When the time elapsed time increases, the temperature should approach to that of classroom temperature. From the graph, we see that the graph that the room temperature must be $20^circ$ C

a) Both graphs appear exponential (decreases sharply and eventually levels off)

b) $85^circ$ C

c) $20^circ$ C

begin{table}[]
defarraystretch{1.5}%
begin{tabular}{|c|c|c|}
hline
begin{tabular}[c]{@{}c@{}}Number of Squares\ on the Chessboardend{tabular} & begin{tabular}[c]{@{}c@{}}Number of Grains\ on that Squareend{tabular} & First Differences \ hline
1 & 1 & \ hline
2 & 2 & $2-1=1$ \ hline
3 & 4 & $4-2=2$ \ hline
4 & 8 & $8-4=4$ \ hline
5 & 16 & $16-8=8$ \ hline
6 & 32 & $32-16=16$ \ hline
7 & 64 & $64-32=32$ \ hline
8 & 128 & $128-64=64$ \ hline
9 & 256 & $256-128=128$ \ hline
10 & 512 & $512-256=256$ \ hline
end{tabular}
end{table}

a) begin{tabular}{|c|c|c|}
hline
begin{tabular}[c]{@{}c@{}}Number of Squares\ on the Chessboardend{tabular} & begin{tabular}[c]{@{}c@{}}Number of Grains\ on that Squareend{tabular} & First Differences \ hline
1 & 1 & \ hline
2 & 2 & $1$ \ hline
3 & 4 & $2$ \ hline
4 & 8 & $4$ \ hline
5 & 16 & $8$ \ hline
6 & 32 & $16$ \ hline
7 & 64 & $32$ \ hline
8 & 128 & $64$ \ hline
9 & 256 & $128$ \ hline
10 & 512 & $256$ \ hline
end{tabular}\\\
b) The graph has been plotted in the answers.\\
c) Both graphs appear exponential since the ratios of the first differences are constant, however, this graph is increasing while the ball-bounce experiment is decreasing.\