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 0.95t (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.
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 0.95t (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.
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:(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 × 0.95¹
(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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