ice loses 1/2 its weight per hour after 8 hours 5/16 of a lb is left, how much did it weigh

Question

ice loses 1/2 its weight per hour after 8 hours 5/16 of a lb is left, how much did it weigh

Answer 1

Since ice loses 1/2 its weight per hour, we can write the following equation 

w(t) = w₀/(2^t) or w₀(2^-t) for

w(t) is the weight if the ice as a function of time in hour

w₀ is the original weight of the ice

t is the number of hours that the ice is left out

 

Also, it was given that after 8 hours, the ice weighs 5/16 lb or w(8) = 5/16. Plug this information into the very first equation and solve fro w₀, which is the original weight of the ice block

w(8) = w₀/2⁸ = w₀/256 = 5/16

w₀ = 80 lb

 

Answer: The ice weighed 80 lbs before it was left to melt