Question

The quantity of new information stored electrically in
2002 was about 5 exabytes, or 5x10^18 bytes. Researchers estimate that this is double what was stored in 1999. Suppose this trend continues. Write and graph a function to predict the pattern of growth beginning in 1999

Answer 1

The function expresses exponential growth and is of the form
\[I _{n}=I _{0}e ^{kt}.............(1)\]
where
\[I _{n}=quantity\ of\ new\ information\]
\[I _{0}=initial\ quantity\ of\ information\]
k is a constant and t is the time in years starting from 1999.
Rearranging equation (1) gives
\[\frac{I _{n}}{I _{0}}=2=e ^{3k}...........(2)\]
Now you need to solve equation (2) to find the value of the constant k. Then the required function can be found by plugging values into equation (1)