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HW 13-preview(2)

# HW 13-preview(2) - Version PREVIEW HW 13 homan(57225 This...

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Version PREVIEW – HW 13 – hoffman – (57225) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. CalC7c44b 001 (part 1 of 3) 10.0 points Jane wishes to bake an apple pie for dessert. The baking instructions say that she should bake the pie in an oven at a constant temper- ature of 160 C . Being a mathematician, she knows that the temperature T of the pie after t minutes of baking will be given by T ( t ) = 160 - Ae kt , where A and k are constants. After 14 min- utes of baking she notices that the tempera- ture of the pie is 96 C , while after 28 minutes it is 128 C . (i) Determine the constants A and k . 1. T ( t ) = (160 - 128 · 2 t/ 14 ) C correct 2. T ( t ) = (160 - 64 · 4 t/ 14 ) C 3. T ( t ) = (160 - 128 · 2 t/ 14 ) C 4. T ( t ) = (160 - 64 · 2 t/ 28 ) C 5. T ( t ) = (160 - 128 · 2 t/ 28 ) C Explanation: Jane’s observations tell us that T (14) = 96 = 160 - Ae 14 k , T (28) = 128 = 160 - Ae 28 k , i.e. , Ae 14 k = 64 , Ae 28 k = 32 . Thus e 14 k = 2 and A = 128. Consequently, T ( t ) = 160 - 128 · 2 t/ 14 . 002 (part 2 of 3) 10.0 points (ii) If the pie is cooked when it reaches a tem- perature of 144 C , how long does it have to be in the oven? 1. cooking time = 42 minutes correct 2. cooking time = 47 minutes 3. cooking time = 37 minutes 4. cooking time = 32 minutes 5. cooking time = 52 minutes Explanation: The length of time t 0 the pie needs to be in the oven is given by T ( t 0 ) = 144 = 160 - 128 · 2 t 0 / 14 . Thus 2 t 0 / 14 = 8. Solving for t 0 we see that cooking time = 42 minutes. 003 (part 3 of 3) 10.0 points (iii) What was the initial temperature of the pie? 1. initial temp = 35 C 2. initial temp = 32 C correct 3. initial temp = 33 C 4. initial temp = 36 C 5. initial temp = 34 C Explanation:

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Version PREVIEW – HW 13 – hoffman – (57225) 2 The initial temperature, T (0), of the pie is given by initial temp = 32 C .
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