Deniz’s computer is infected with a virus that will erase information from her hard drive. It will erase information quickly at first, but as time goes on, the rate at which information is erased will decrease. In t minutes after the virus starts erasing information, $5,000,000(\frac { 1 } { 2 })^t$ bytes of information remain on the hard drive.

1. Before the virus starts erasing, how many bytes of information are on Deniz’s hard drive?

   Answer (a):

   $5,000,000$ bytes

2. After how many minutes will there be $1000$ bytes of information left on the drive?

   Hint (b):

   Set the given function equal to $1000$ and solve for $t$.

   Answer (b):

   $≈ 12.3\ \text{minutes}$

3. When will the hard drive be completely erased?

   Hint (c):

   What is the smallest number of bytes possible before the hard drive is completely erased? Solve for $t$.