A tropical water lily doubles in size each week. If it takes 60 weeks for the plant to completely cover a pond, when will half the pond be covered?
59 weeks
Is it how?
If the water lily covers half the pond on one day, then it doubles its size the next day to completely cover the pond.
Thank you!!!
You're welcome.
I see I made an error -- it should be doubles its size the next week.
To determine when half the pond will be covered, we need to find the number of weeks it takes for the water lily to cover half of the pond's surface area.
Since the water lily doubles in size each week, the surface area covered will also double. Therefore, we can use a reverse process to determine when half the pond will be covered.
Let's start by assigning variables:
- Let x represent the number of weeks it takes for half the pond to be covered.
- Let S represent the surface area of the pond.
We know that the water lily doubles in size each week, so after x weeks, it will cover 2^x times the initial surface area.
We also know that it takes 60 weeks for the pond to be completely covered. Therefore, at week 60, the water lily will cover the entire pond, which means it will cover 2^60 times the initial surface area.
To find when half the pond will be covered, we need to solve the equation: 2^x = 2^60 / 2
First, simplify the right side of the equation: 2^60 / 2 = 2^59
Now, we have the equation: 2^x = 2^59
Since the bases are equal, the exponents must also be equal. Therefore, x = 59.
Hence, it will take 59 weeks for half the pond to be covered by the water lily.