the US food and drug administration uses this mathematical model for the number of bacteria B in food refrigerated at temperatures T (celsius);
B = 20 T^2 - 20T + 120
The temp in a particular refrigerator can be set anywhere between -2 degree celcius and 14 degree celcius. Determine the temperature where the number of bacteria will be at minimum
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B = 20T² - 20T + 120 , At temperature = 0.5°C the number of bacteria will be minimum
Step-by-step explanation:
B = 20T² - 20T + 120
-2 ≤ T ≤ 14
dB/dT = 40T - 20
dB/dT = 0
=> 40T - 20 = 0
=> T = 1/2
d²B/dT² = 40 ( + ve)
Hence T = 1/2 will give minimum Value of Bacteria
T = 1/2
B = 20 (1/2)² - 20T + 120
=> B = 5 - 10 + 120
=> B = 115
At temperature = 0.5°C the number of bacteria will be minimum
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