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Question 158984: Help, I am confused!!!
I have to solve the following problem involving applications of polynomials:
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, that it records each pixel in x-bit color, that there are 26 frames recorded per second, and that each frame is recorded in 1600 x 1200 resolution.
I. 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)
II. Evaluate this function for x=32 (32-bit true color)
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! here's what i have.
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80 GB hard drive equals 80 * 10^9 bytes (not bits) capacity.
since there are 8 bits per byte, the hard drive capacity in bits would then be
80*8*10^9 Gb hard drive capacity (Gb = 1 gigabit; GB = 1 gigabyte)
if you let C = capacity of the hard drive in Gb, then
C = 80*8*10^9
C = 6.4 * 10^11
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1200 x 1600 resolution per frame equals 1.92 * 10^6 pixels per frame since the number of pixels per frame is calculated by taking 1200 and multiplying it by 1600.
if you let P = pixels and F = frame, then
P/F = 1.92*10^6
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there are 26 frames per second in a video picture.
if you let S = seconds, then
S = 26*F
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if you want to know how many frames in a minute, you would take the number of frames per second and multiply it by 60.
if you let M = minutes, then
M = 60*S = 60*26*F
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x-bit color refers to the number of bits that are used per pixel to represent color.
2-bit color means 2 bits per pixel.
32-bit color means 32 bits per pixel.
x-bit color means x bits per pixel.
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if you want to know how many bits per frame you would take pixels per frame and multiply it by the number of bits per pixel.
let B/P = number of bits per pixel.
B/P = x
let B/F = (P/F)*(B/P)
from above, P/F = 1.92*10^6
from here, B/P = x
B/F = 1.92*10^6*x
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if you want to know how many bits per minute, you would take bits per frame and multiply it by number of frames per second and multiply that by 60 seconds.
B/F = 1.92*10^6*x
let B/M = bits per minute
B/M = B/F*(F/S)*60
B/F = 1.92*10^6*x
F/S = 26
B/M = 1.92*10^6*x*26*60*x
B/M = 2.9952*10^9*x
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formula for number of minutes of video that can be stored on the hard drive becomes C / (B/M)
6.4 * 10^11 / 2.9952*10^9*x = 213.6752137/x
answer is 213.6752135/x minutes of video.
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if you let x = 32 bits, then number of minutes of videos becomes
213.6752137/32 = 6.677350427 minutes of video at 32 bits per pixel.
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