Question 730245: In a lake, there is a patch of lily pads. Every day the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?
Found 3 solutions by lynnlo, ikleyn, MathTherapy:
Answer by lynnlo(4176)   (Show Source):
Answer by ikleyn(53427)  (Show Source):
You can put this solution on YOUR website! .
In a lake, there is a patch of lily pads. Every day the patch doubles in size.
If it takes 48 days for the patch to cover the entire lake, how long would it take
for the patch to cover half of the lake?
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It is a classic puzzle for those who start learning exponential functions.
The correct answer is 47 days.
The solution to this puzzle is extremely short:
If the patch covers the entire lake in 48 days, it means that
half of the lake is covered in the previous, 47-th day.
What is interesting: the correct answer and this short solution often shock the beginners.
But don't be discouraged - this is a normal reaction for a beginner.
That's why you're learning from experts to understand non-obvious truths.
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The answer "24" in the post by @lynnlo is incorrect.
Answer by MathTherapy(10587)  (Show Source):
You can put this solution on YOUR website!
In a lake, there is a patch of lily pads. Every day the patch doubles in size. If it takes 48 days for the patch to cover
the entire lake, how long would it take for the patch to cover half of the lake?
I wholeheartedly agree with Tutor @Ikleyn that the patch will take 47 days to cover  of the lake, considering
that its growth DOUBLES every day.
For this exponential growth scenario, we need to use the Simple Discrete Growth Formula:  , or  , where:
f(x) = Growth percent/fraction at a particular time (max being 100, or 1, or  )
x = time period during growth
a = Initial/Beginning growth percent/fraction ( )
b = growth rate <=== this can also be represented by 1 + r
 ---- Substituting 48 for x, and 2 for b
 ---- Substituting 1 (100%) for f(48)
Initial percent/fraction of lake covered, or a = 
 ----- Substituting for a, and 2 for b
 ----- Substituting for f(x)
 -- Converting to  , and to 
- 1 = - 48 + x ----- BASES are equal, and so are the exponents
Time it takes for the patch to cover of the lake, or x = - 1 + 48 = 47 days.
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