In this question, you should round answers appropriately where necessary. (a) A hardware engineer is looking at the temperature of Central Processing Units (CPUs) of different computers. In one experiment, the temperature of the CPU of her own computer can be modelled by the equation y = -0.05t +45 (0 ≤ t ≤ 60). where y is the temperature of the CPU in degrees Celsius and t is the number of seconds into the experiment. (i) Find the temperature of the CPU after 17 seconds according to this model. (ii) Explain what is meant by the inequality (0 ≤t≤60)' that follows the equation. (iii) Using algebra, calculate the time at which the CPU is 42.6° C. (iv) Write down the gradient of the straight line represented by the equation y = -0.05t +45. What does this measure in the practical situation being modelled? (v) What is the y-intercept of the equation y = -0.05t + 45? Explain what it means in the practical situation being modelled. (b) The same engineer decides to look into rates of cooling for liquids to experiment with different cooling solutions for servers. She finds that the rate of cooling for one liquid can be modelled by the equation: y=97 x 0.95€ (0
In this question, you should round answers appropriately where necessary. (a) A hardware engineer is looking at the temperature of Central Processing Units (CPUs) of different computers. In one experiment, the temperature of the CPU of her own computer can be modelled by the equation y = -0.05t +45 (0 ≤ t ≤ 60). where y is the temperature of the CPU in degrees Celsius and t is the number of seconds into the experiment. (i) Find the temperature of the CPU after 17 seconds according to this model. (ii) Explain what is meant by the inequality (0 ≤t≤60)' that follows the equation. (iii) Using algebra, calculate the time at which the CPU is 42.6° C. (iv) Write down the gradient of the straight line represented by the equation y = -0.05t +45. What does this measure in the practical situation being modelled? (v) What is the y-intercept of the equation y = -0.05t + 45? Explain what it means in the practical situation being modelled. (b) The same engineer decides to look into rates of cooling for liquids to experiment with different cooling solutions for servers. She finds that the rate of cooling for one liquid can be modelled by the equation: y=97 x 0.95€ (0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:In this question, you should round answers appropriately where necessary.
(a) A hardware engineer is looking at the temperature of Central Processing
Units (CPUs) of different computers. In one experiment, the
temperature of the CPU of her own computer can be modelled by the
equation
y = -0.05t +45 (0 ≤ t ≤ 60).
where y is the temperature of the CPU in degrees Celsius and t is the
number of seconds into the experiment.
(i) Find the temperature of the CPU after 17 seconds according to this
model.
(ii) Explain what is meant by the inequality (0<t≤60)' that follows
the equation.
(iii) Using algebra, calculate the time at which the CPU is 42.6° C.
(iv) Write down the gradient of the straight line represented by the
equation y = -0.05t +45. What does this measure in the practical
situation being modelled?
(v) What is the y-intercept of the equation y=-0.05t +45? Explain
what it means in the practical situation being modelled.
(b) The same engineer decides to look into rates of cooling for liquids to
experiment with different cooling solutions for servers. She finds that
the rate of cooling for one liquid can be modelled by the equation:
y=97 x 0.95² (0 ≤t≤80)
where y is the temperature of the liquid in degrees Celsius and t is the
time in minutes.
(i) State whether the type of reduction for this model is linear or
exponential. Describe how reduction rate differs between linear and
exponential functions.
(ii) Calculate the temperature when t = 15.
(iii) Write down the scale factor and use this to find the percentage
decrease in the temperature per minute.
(iv) Use the method shown in Subsection 5.2 of Unit 13 to find the time
at which the temperature is 35° C.
(v) Determine the halving time of the temperature.
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