lily pads and how many days

Question

Lily pads on the MS state lake double everyday.  If the lake is completely covered on day 30, on what day was the pond half full?

Answer 1

It was half covered on the 29th day.

 

Suppose that

X lily pads cover the lake

  

 The function is f(N) = k*2^n since they double every day

 

 k*2^30 = X ---> k = X/2^30

 

 SO f(n) = (X/2^30)*2^N

 

             = X* 2^(N-30)

 

 

Finally

  X*2^(N-30) = X/2

 

 2*X*2^(N-30) = X

 

 X*2^(N-29) = X

 

  2^(N-29) = 1

 

N-29 = 0

 

N=29

 

So on the 29th day, the pond was half covered.

 

That is

 

 f(29) = X*2^(29-30) = X * 2^(-1) = X/2

 

On the 30th day, 

 

f(30) = X*2^(30-30) =X*2^0 = X*1 = X