Plllllllllllllllllllllllz help me wid dis (math)?

A water lily growing in a circular pond doubles in size every day. It takes thirty days to cover the whole pond. How long does it take to cover half the pond?

Plllllllllllllllllllllllz help me wid dis (math)?
Well, think about it logically. it doubles in size every day. on the 30th day, it is equal to the size of the pond. so in comparison to the pond, how big is it on the 29th day. well since it doubled from the 29th to the 30th, it must be 1/2 of the 30th. well half the 30th (the whole pond) is half the pond. so it will take 29 days to cover half the pond.



Mathematically: this describes a geometric sequence (something is being changed by multiplying by the same thing each time, in this case doubles so multiplying by 2 each time)



the geometric formula is:



final = initial(r)^(n-1)



r=ratio =2 for this problem



let's say the pond is x

the beginning is 1

n=30 (number of days)



x = 1(2)^29



Then half the pond would be x/2



x/2 = 1(2)^a-1

plug in x

2^29/2 = 2^a-1

2^28 = 2^a-1

therefore, we have the same base, so the exponents are equal



28 = a-1

a =29 days
Reply:29. If it doubles in size every day, then the 29th day would be half the size as the 30th day (the day when it covers the whole pond).
Reply:on the 29th day the liliy will cover half the pond. On the 30th day when it doubles its size the full pond will be covered.
Reply:it doubles in every day so the lily take 30 days to cover the whole one it will take 29 days to cover the whole pond because it covered half the pond in the 29 day and the remainig half in the 30th day.
Reply:Yep, what they said!!
Reply:If it doubles in size every day, then it was half the size of the pond the day before it covered the whole pond. So, 29 days.
Reply:15 days? haha. i dunoe. where are u from by the way? singapore?

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