SOLUTION: George Lucas pioneered the use of digital movie cameras with the most recent Star Wars film. Assume that Lucas's camera has a swappable 80 GB hard drive (remember: 1 GB = 1024 MB,
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Question 83368: George Lucas pioneered the use of digital movie cameras with the most recent Star Wars film. Assume that Lucas's camera has a swappable 80 GB hard drive (remember: 1 GB = 1024 MB, 1 MB = 1024 KB, 1 KB = 1024 Bytes, and 1 Byte = 8 bits), that it records each pixel in x-bit color, that there are 26 frames recorded per second, and that each frame is recorded in 1600x1200 resolution.
Create a polynomial function that gives the number of minutes of video that can be recorded before swapping in a new hard drive, as a function of x (the number of bits used to encode the color of each pixel)
Evaluate this function for x = 32 (32-bit true color) Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! T = minutes of video before hard drive is filled up
80 Gb * 8 bits/byte / T sec = (x bits/pixel)(pixels/frame)(frames/sec)
Multiplying both sides by T sec
(T sec)(x bits/pixel)(pixels/frame)(frames/sec) = 80 Gb * 8 bits/byte
T sec = (80 Gb * 8 bits/byte) / (x bits/pixel)(pixels/frame)(frames/sec)
The function x is required to be in minutes, so multiply each side
by 1/60 min/sec
(T sec)(1/60 min/sec) =
(80 Gb * 8*1024^3 bits/Gbyte) / (bits/pixel)(pixels/frame)(frames/sec)(sec/min)
This is in the form T = f(x). I'll check the units by shortening the units
to one letter. Notice that (1/60 min/sec) ends up being (60 sec/min) on
the right side because it's in the denominator
(s)(m/s) = (Gbyte)(b/Gbyte) / (b/p)(p/f)(f/s)(s/m)
I cancel units, and I,m left with
m = m, so now I plug in actual numbers
The 1024^3 comes from:
1024 bytes/Kbyte
1024 Kbytes/Mbyte
1024 Mbyte/Gbyte
multiply both sides by 60 min answer for function
If x = 32,
Dividing by 60 min/hr, I get
7 hrs 10 min 11 sec answer
Unless I made a mistake, and I certainly could have
