Someone please explain this to me?

Question

A gardener plants a Water Lilly in a pond. The lilly doubles in size every day. After 16 days the entire pond is covered by the plant.

a) If the area of the pond is 32,768 square feet, what was the original size of the plant?

b) After how many days was the pond half covered?

-- I dont understand how to figure this out. Im not asking for answers, just someone to explain to me how to do this. Thank you!

Answer 1

I think you keep dividing by 2. So:

32768-day 16
16384-day 15
8192-day 14
4096-day 13
2048-day 12
1024-day 11
512-day 10
256-day 9
128-day 8
64-day 7
32-day 6
16-day 5
8-day 4
4-day 3
2-day 2
1-day 1

The trick is not to simply divide by 16. The plant started out 1 square foot. 15 days until the lilly covers half the pond. It doubles over night, and on the 16th day covers the pond. I'm not 100% sure, but I think that's how it's done.

Answer 2

The thing to notice here is that 32,768 is 2^15th power. So if the lily started at 1/2 square foot, in 1 day it would be 1 square feet (2^0), in 2 days it would be 2 square feet (2^1), ... and in 16 days it would be 2^15 square feet, namely the size of the pond. So it started at 1/2 square foot (2^-1). The pond was half covered the day before the 16th day, because on that last day it doubled in size.

Answer 3

Hi

So start by assigning an unknown variable to the size of the lilly. Say x.
You know at the end of every day the size is two times what it was before. So if the number of days is n, then the size of the lilly is ... (2^n)*x. Its easy to see this if you actually experiment and plug some numbers in.
Say the size of the lilly was 1. Then the sequence of size each day would look like this:
1, 2, 4, 8, 16, 32.....

Now you have a two-variable equation and some conditions. Plug in the numbers and solve!

Answer 4

every day, the plant grows to be 2 raised to the power of the day. i.e. after day 1, 2 to the 1st power is 2, so it has doubled by the second day.

after day 2, 2 to the 2nd power is 4 so it has grown to 4 times its original size by the 3d day.

after day 15 (i.e. on the 16th day), it has grown to be 2 to the 15th power of its original size. so, if 2^15= 32,768, the original size must have been 1 square foot!

also, the pond was 1/2 covered the day before, i.e. on the 15th day!

Answer 5

Hi there!
If it doubles every day, so on day 2 it will be 2*x, x being surface on the first day.
On day 3 it will be 2*2x
On day 4 it will be 2*2*2x
....
On day 16 it will be 2*2*2..... (how many? write it down and figure it out. :)) What's the x then?

If it doubles every day, half covered would occur the day before the last day, because on last day it will double to the entire area.
(So day 15.) uuups, I now answered your second question. Sorry :)

Hope I helped....

Answer 6

the process is geometric progression...

the original size was 1 square foot...

it doubled each day...the pond was half covered in 14 days...

progression...1,2,4,8,16,32,64, etc.

Answer 7

ok, do 32,768 dixided by 16. now i juss didd 32768 divided by 16=2048. then i didd 2048 times 14 which is 32768.so im guessing it was 7 or 8 days that it was half covered, butt idk, im no math genius! lol good luk!