Question 285532: A lily pad grows so that each day it doubles its size (area). On the 20th day of its life, it completely covers the pond. On what day of its life was the pond half covered?
A. 5th B. 10th C. 15th D. 19th E. None of these.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! It starts its life on day 0
On day 1 it is double in size.
On day 2 it is double in size again.
Assume it's size is 1 unit at birth.
On day 1 it's size is 2 units in size.
On day 2 it's size is 4 units in size.
etc.
Formula is 1 * 2^n where n is the number of days of its life.
On day 1, it is 1*2^1 = 2 units in size.
On day 2, it is 1^2^2 = 4 units in size.
On day 20, it is 1^2^20 = 1048576 units in size.
The pond is covered when the lily pad is 1048576 units in size.
The pond is half covered when the lily pad is 1048576/2 = 524288 units in size.
The number of days it takes for the lily pad to become 524288 units in size is given by the formula:
524288 = 1 * 2^x
you need to solve for x.
Take the log of both sides of this equation to get:
log(524288) = log(1*2^x)
Since 1*2^x is the same as 2^x, this equation becomes:
log(524288) = log(2^x)
Since log(2^x) = x*log(2), this equation becomes:
log(524288) = x*log(2)
Divide both sides of this equation by log(2) to get:
log(524288)/log(2) = x
Solve for x by using the log function of your calculator to get:
x = 19
The pond was half covered with the lily pad on the 19th day.
You could also have figured that out a lot more easily by noting that the lily pad was doubling in size each day, so if it fully covered the pond on the 20th day, it had to have half covered the pond the day before. All it took was one more day.
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