15 Growth and Decay

15 Growth and Decay - 15. GROWTH AND DECAY 1. A potato is...

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Unformatted text preview: 15. GROWTH AND DECAY 1. A potato is put into an oven whose temperature remains constant at 200 C. The temperature H of the potato changes according to ) 200 (-- = H k dt dH where k is a positive constant. Here H is measured in C and time t is measured in minutes. The temperature of the potato is 20 C when it is placed in the oven. After 30 minutes the temperature of the potato is 120 C. (a) [7 marks] Find k . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (b)[3 marks] The potato is ready to be eaten when its temperature is 180 C. How many minutes after it has been placed in the oven will this occur? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET Calculus 92 15. Growth and Decay 2. A bacterial culture is placed in a large glass bottle. The volume of the culture doubles every hour, and the culture fills the bottle after 24 hours. (a) [2 marks] If the culture is placed in the bottle at time t = 0, when does the culture half fill the bottle? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (b)[8 marks] While the volume of the culture is less than 1% of the volume of the bottle, the culture is not visible. After this stage of growth the culture is visible. If the culture is placed in the bottle at time t = 0, how long does it take for the culture to become visible? = 0, how long does it take for the culture to become visible?...
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15 Growth and Decay - 15. GROWTH AND DECAY 1. A potato is...

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