SOLUTION: The number of fruits in a basket doubles every minute. The basket is full of fruits in one hour. When was the basket one eightth full?

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Question 982510: The number of fruits in a basket doubles every minute. The basket is full of fruits in one hour. When was the basket one eightth full?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of fruits at start
+n+ doubles every minute for +60+ min
------------------
start: +n+
1 min: +2n+
2 min: +4n+
3 min: +8n+
. . . . . . . . . . . .
60 min: +%28+2%5E60+%29%2An+
---------------------
Let +k+ = time in min when basket
is 1/8 full
Find:
+%281%2F8%29%2A%28+2%5E60+%29%2An+=+%28+2%5Ek+%29%2An+
+2%5Ek+=+%28+1%2F8+%29%2A2%5E60+
+%28+2%2Ak+%29%2A%28+2%5E3+%29+=+2%5E%28+60+%29+
+2%5E%28+k+%2B+3+%29+=+2%5E%28+60+%29+
+k+%2B+3+=+60+
+k+=+57+
After 57 min the basket was 1/8 full
-----------------
check:
Suppose +n+=+1+
I want to show:
+2%5E57+=+%281%2F8%29%2A2%5E60+
+2%5E%28+60-57%29+=+8+
+2%5E3+=+8+
+8+=+8+
OK