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

1). If the algae doubles every day, it will take 15 days for it to cover half the lake. This means it would happen on January 15.

2). Your friend may be skeptical because they may not believe that the algae can grow so quickly and cover the entire lake in just 30 days. Alternatively, they may not believe that you have accurate information about the situation.

3). Removing most of the algae on January 29 would significantly reduce the amount of algae in the lake and would likely help prevent the lake from becoming completely covered. However, if 1% of the surface is still covered with algae on February 1, it is possible that the problem has not been fully solved and the algae could continue to grow and potentially become a problem again in the future. It would be best to continue monitoring the lake and taking action to prevent the algae from growing.