How many lilies does it take to cover?

Question

A particular lake has water lilies growing on it. On the first day, there are two water lilies. Each day, the number of water lilies doubles. After 30 days, the water lilies cover half the lake. How many days will it take to cover the entire lake?

How many lilies does it take to cover half the lake?

 

Answer both questions and Show work please.

Answer 1

Assume a surface area of the water lily is S, lake surface area L, the key equations is:

S(2³⁰)=L/2

multiplying by 2:

S(2x2³⁰)=L, or S(2³¹)=L

 

thus it will take 31 days and 2³¹ lilies to cover the entire lake.