Due to melting, an ice sculpture loses one-half its weight every hour. After 8 hours, it weighs 5/16 of a pound. How much did it weigh in the beginning?
2007-10-08 16:35:35 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Since it loses 1/2 its weight every hour, it was twice as heavy an hour ago as it is now.
So
now ... 5/16 lbs
1hr ago ... 5/8 lbs
2 hrs ago ... 5/4 lbs
3 hrs ago ... 5/2 lbs
4 hrs ago ... 5 lbs
5 hrs ago ... 10 lbs
6 hrs ago ... 20 lbs
7 hrs ago ... 40 lbs
8 hrs ago ... 80 lbs
I hope this helps!
2007-10-08 16:42:35 · answer #1 · answered by math guy 6 · 0⤊ 0⤋
You can argue by doing this discretely.. like on an hourly basis working backwards...
8 hours == 5/16
7 hours == 5/8
6 hours == 5/4
etc..
but the problem here is that between 6 1/2 and 7 1/2 hours the weight should follow the rule that
wt decreases to half every hour. This computation will not fit that.
===========================
Hence, you have to use exponential decay here.
y = A e^(kt)
where after A is the initial wt. , y is the wt after t hours, and k is your decay constant
After 1 hr, the ice sculpture should have only half of its original wt, thus
A/2 = A e^(k) ... (note t = 1)
1/2 = e^k .... (cancel A)
hence k = ln (1/2) OR k = -0.69
Now you can get the original wt A. Since after t=8 hrs, the ice sculpture is only 5/16 pounds, then
5/16 = A * e^( (-0.69) (8) )
5/16 = A * 0.00407
A= 76.71 pounds..
2007-10-08 23:53:41 · answer #2 · answered by rommelA 2 · 0⤊ 0⤋
OK -- From an algebraic standpoint
1/2^8 x = 5/16
1/256 x = 5/16
x = 5/16 * 256
x = 80
So the statue originally was 80 lbs.
Hope this helps.
2007-10-08 23:45:42 · answer #3 · answered by pyz01 7 · 0⤊ 0⤋
By the concept of half-life, after 8 hours, the sculpture weights 1/256 th of its original weight.
Then the original sculpture weighed 80 pounds.
(I wonder what the sculpture was).
2007-10-08 23:41:33 · answer #4 · answered by cattbarf 7 · 0⤊ 0⤋
Suppose the initial weight is x pound.
As it looses one half of its weigh in every hour, in eight hour it looses (x divided by 2 to the power 8) that is x / 256, which is now equal to 5/16 pounds. now solve it:
x/256 = 5/16
So, x that is the initial weight is 80 pounds.
2007-10-08 23:48:52 · answer #5 · answered by rd 1 · 0⤊ 0⤋
y = Ae^kt .. you have to recognize that you have an exponential function...
if t = 1, y = A/2
A/2 = A e^k ... e^k = 1/2
y = A (1/2)^t
if t = 8...
y = A (1/2)^8 = 5/16
A = (5/2^4) * 2^8 = 80 pounds.
§
2007-10-08 23:43:02 · answer #6 · answered by Alam Ko Iyan 7 · 0⤊ 0⤋
I was never any any good at related rate problems.
2007-10-08 23:39:29 · answer #7 · answered by cartiphilus 4 · 0⤊ 2⤋