Snow begins to fall at noon. After one hour, 2.45 cubic feet of snow are accumulated on the surface
of a small frozen lake. If the amount of snowfall increases by 15% each hour, find the amount of
snow, in cubic feet, on the surface of the lake at midnight of the day

Question

Snow begins to fall at noon.  After one hour, 2.45 cubic feet of snow are accumulated on the surface 
of a small frozen lake.  If the amount of snowfall increases by 15% each hour, find the amount of 
snow, in cubic feet, on the surface of the lake at midnight of the day

dumbcow · Answer

geometric series
$$S = 2.45+2.45(1.15)+2.45(1.15)^{2}+...2.45(1.15)^{11}$$
sum formula for geometric series gives
$$S = 2.45*\frac{(1.15)^{12} -1}{1.15 -1}$$