Assume that water lilies double in area every 24 hours. In the spring, there is one water lily on a lake. After thirty days, the lake is completely (100%) covered with water lilies. How many days did it take for lilies to cover 25% of the lake?
now: 1 lily
after 1 day: 2 lilies = 2^1
after 2 days: 4 lilies = 2^2
...
after 30 days : 2^30
this is 100%, so 25% would be 2^30/4 = 2^28
2^28 = (2)^t
t = 28
or simply work backwards....
in 30 days it was 100% covered
in 29 days it was 50% covered
in 28 days it was 25% covered.
Are you sure this is not the question from the pioneer woman's quiz for an ipad??
To solve this problem, we need to find the number of days it took for the water lilies to cover 25% of the lake. Since the water lilies double in area every 24 hours, we can divide the problem into smaller steps.
Step 1: Determine the number of times the water lilies would double in area to cover 100% of the lake.
Since the water lilies double in area every 24 hours, after 24 hours, they would cover 2 times their initial area. After 48 hours, they would cover 4 times their initial area. Continuing this pattern, after 30 days (which is equal to 30 * 24 = 720 hours), the water lilies would cover 2^30 times their initial area.
Step 2: Calculate the area covered by the water lilies after 30 days.
Since the number of water lilies doubled in every 24 hours, the area covered by the water lilies after 30 days is 2^30 times their initial area.
Step 3: Calculate the number of times the water lilies need to double to cover 25% of the lake.
To find out how many times the water lilies need to double, we need to determine the area covered by the water lilies when they cover 25% of the lake. 25% of the lake is equal to 0.25 times the initial area.
Step 4: Find the number of days required for the water lilies to cover 25% of the lake.
Since the water lilies double every 24 hours, we need to find the number of times the water lilies will double to cover 25% of the lake. We can calculate this by taking the logarithm base 2 of 0.25 (which represents the number of times the water lilies need to double) and divide it by 30 (to convert it into days).
Using these steps, let's calculate the number of days it took for the water lilies to cover 25% of the lake:
Step 1: 2^30 = 1,073,741,824.
Step 2: The water lilies covered 1,073,741,824 times their initial area after 30 days.
Step 3: 0.25 * initial area = 1,073,741,824 times initial area.
Step 4: log base 2 (1,073,741,824) / 30 = 5.
Therefore, it took 5 days for the water lilies to cover 25% of the lake.
To find out how many days it took for water lilies to cover 25% of the lake, we can work backwards from the given information.
Let's start with the fact that the lake was completely covered with water lilies after 30 days. This means that on day 29, the lake was 50% covered with water lilies, and on day 28, it was 25% covered.
Since the water lilies double in area every 24 hours, we can divide the number of days it took to cover 25% (day 28) by 2 to find when the lake was 12.5% covered. Half of 25% is 12.5%.
So, it took 14 days for the water lilies to cover 12.5% of the lake.