The area covered by water lilies in a pond you own doubles in size every day. If allowed to grow the plants would cover the entire pond surface in 30 days. You had decided to do nothing until the pond is ½ covered.
a. On what day will the pond be ½ covered?
b. How long do you have before you must act or have your pond covered with the plants?
a. The pond will be 1/2 covered on the 29th day.
i got that but i was not sure about b)b. How long do you have before you must act or have your pond covered with the plants?
30 - 29 = ?
I don't know either could you help me today? like now
To solve this problem, we can work backwards from the day when the entire pond surface is covered.
a. On what day will the pond be ½ covered?
Since the area covered by water lilies doubles every day, we can conclude that on the day before the pond is fully covered, it would be half covered. So, to find the day when the pond is half covered, we need to find the number of days before the 30th day.
To do this, we can use the concept of exponential growth. If the area covered by water lilies doubles every day, then on the day before the pond is fully covered, it would be half covered.
Let's assume the initial area covered by water lilies is represented by "A". On the first day, A doubles to 2A, on the second day, it doubles again to 4A, and so on.
On the day before the pond is fully covered, it would be half covered, which means the covered area would be equal to half of the total pond surface area. Let's call this half-covered area "B".
On the 30th day, the entire pond surface is covered, so it would be equal to 30A.
So, we can set up the following equation:
30A = B
But B is equal to half of the pond's surface area, so we can write:
30A = (1/2) * A
By canceling out A from both sides of the equation, we get:
30 = 1/2
To solve for A, we can divide both sides by 30, giving us:
A = 1/60
Now that we know the initial area covered by water lilies is 1/60 of the pond's surface area, we can deduce that on the day before the pond is fully covered (which is the day when it is half covered), the area covered by water lilies would be 1/120 of the pond's surface area.
b. How long do you have before you must act or have your pond covered with the plants?
Since we have determined that on the day before the pond is fully covered, it would be half covered (which is 1/120 of the pond's surface area), we can conclude that you still have 29 days before you must act.
Therefore, the pond will be half covered on the 29th day, and you have 29 days before the entire pond is covered with water lilies.