MATHEMATICS: a flower grows in a lake...?

A small circular flower located in the centre of a circular lake. The flower's surfuce (lets say its leaves) expands twice as much compared to every previous day (suppose its surfuce is negligible the the day it starts to grow) and it's covered the whole lake in 20 days. Which day the flower had covered the half of the lake's surfuce?
MATHEMATICS: a flower grows in a lake...?
day 19th
Reply:Day 19





If the flower covers the lake on day 20 then the previous day the flower surface was half as big and therefore covered half the lake
Reply:yes, day 19
Reply:Day 19





It will expand double the next day.
Reply:19th day.
Reply:19th day. The next day it doubles in size to cover all the lake
Reply:the tenth!


God knows. Mail me the answer please, coz that sort of thing bugs the sh*t out of me!
Reply:starting size of flower = k sq units say,





after 1st day,flower has covered 3k sq units





after nth day,flower has covered (2^(n+1)-1)k sq units





after 20 days,flower has covered(2^21-1) k sq units ,the area of the lake





half the area of lake =(2^21-1)/2 k





let m = time taken for flower to cover half the lake





therefore,(2^(m-1)-1)k = (2^21-1)/2k





%26gt;%26gt;%26gt;%26gt;%26gt;%26gt;%26gt;2^(m-1)-1 = 2^20-1/2





%26gt;%26gt;%26gt;%26gt;%26gt;%26gt;%26gt;%26gt;%26gt;%26gt;m-1 %26gt; 20





m %26gt; 19





therefore, it takes slightly more than 19 days for the flower to cover half the lake
Reply:don't flowers have petals? i would also go for 19days.
Reply:The 19th day!
Reply:I'm not too sure about such questions, but I'll try to give the answer I think best suits this.





Lets just take the original area of the flower as "x". Thus, the flower's growth by day "y" will be given by,





Area of flower by day "y" = x(2^y)





Thus,





Area covered at the end of 20 days, or the surface area of the lake will be given as,





Lake Surface Area


= x(2^20)


= 1048576x





Half Lake Surface Area


= 524288x





Since x is a constant, we will neglect it's presence. So thus, half the surface area of the lake is 524288 units.





Area of flower = 2^y, where "y" is the number of days,


524288 = 2^y


lg 524288 = lg (2^y)


lg 524288 = y*lg 2


y = (lg 524288)/(lg 2)


y = 19





Thus, mathematically, it takes the flower 19 days to cover the lake by half.





I hope I will receive feedback on my solution... =)
Reply:perhaps you mean petals petal...19th day half....18th day quarter...17th day eightth...16th day sixteenth...15th 1/32..14th 1/64..13th 1/128....12th 1/256...11th 1/512...10th 1/1024 etcetc interesting
Reply:more of a riddle than a maths question.





kinda gave it away with the original area being negligible otherwise you could say A= Ai x2^d





but you'd need to know the area of the lake and the original area
Reply:Getting myself ready to answer this question, till i read someones answer.





yes obviously its the19th day, cos it will have doubled on the 20th day so half the lake covered by day 19.
Reply:19 daysvisual arts