In this question, you should round answers appropriately where necessary. (a) A hardware engineer is looking at the temp

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In This Question You Should Round Answers Appropriately Where Necessary A A Hardware Engineer Is Looking At The Temp 1 (90.82 KiB) Viewed 56 times

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 +47 (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 32 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 45.8° C. (iv) Write down the gradient of the straight line represented by the equation y = -0.05t + 47. What does this measure in the practical situation being modelled? (v) What is the y-intercept of the equation y = -0.05t + 47? 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 = 48 x 0.997 (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. (i) Calculate the temperature when t = 20. (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 30°. (v) Determine the halving time of the temperature.