Question

On January 1, a nasty species of algae is mistakenly introduced into Lake Skinner. It grows in such a way that it doubles every day. If it continues to grow like this, the lake will be totally covered and the fish in the lake will suffocate. At the rate it is growing, this will happen on January 30.

1). When will Lake Skinner be covered halfway?
2). On January 26, you convince your friend that the lake will be completely covered soon. Your friend laughs. Why is your friend skeptical?
3). One January 29 a cleanup crew arrives and is able to remove most of the algae. When they are done on February 1, only 1 % of the surface is covered. How well does this solve the problem in Lake Skinner?

Answer 1

Answer: If the algae in Lake Skinner doubles every day, then on the 15th day (halfway between the 1st and 30th) the lake will be covered halfway.

If the algae doubles every day, then on January 26 it would have only doubled six times, meaning it would only cover 1/64 of the lake's surface. This is why your friend may be skeptical that the lake will be completely covered soon.

The cleanup crew's efforts on January 29 were able to remove most of the algae, but by February 1 only 1% of the lake's surface was still covered. This means that while the problem has been greatly reduced, it is not completely solved and there may still be some risks to the fish in the lake. Continued monitoring and efforts to prevent future algae blooms may be necessary to fully protect Lake Skinner.

Explanation: