An electronically controlled thermostat in a home is programmed to lower the tem

Question

An electronically controlled thermostat in a home is programmed to lower the temperature automatically during the night. The temperature in the house T (in degrees Fahrenheit) is given in terms of t, the time in hours on a 24-hour clock (see figure).

An electronically controlled thermostat in a home is programmed to lower the temperature automatically during the night. The temperature in the house T (in degrees Fahrenheit) is given in terms of t, the time in hours on a 24-hour clock (see figure) 0 2. 50 1 3 6 9 12 15 18 21 24 Time (in hours)

Explanation / Answer

(e)

for 0 t 6,T(t)=60

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for 6<t<7 ,

T(t)=60+ ((72-60)/(7-6))(t-6)

T(t)=60+ (12)(t-6)

T(t)=60+ 12t -72

T(t)=12t -12

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for 7 t 20,T(t)=72

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for 20< t< 21,T(t)=72+ ((60-72)/(21-20))(t-20)

T(t)=72+ (-12)(t-20)

T(t)=72-12t+240

T(t)=312-12t

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for 21 t 24,T(t)=60

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