121616949-math.246

# 121616949-math.246 - how much is left after 6000 years How...

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232 Chapter 9 Applications of Integration 14. Suppose that ˙ y = ky , y (0) = 1, and ˙ y (0) = 3. What is k ? Compute y (4). 15. A radioactive substance obeys the equation ˙ y = ky where k < 0 and y is the mass of the substance at time t . Suppose that initially, the mass of the substance is M > 0. At what time does half of the mass remain? (This is known as the half life. Note that the half life depends on k but not on M .) 16. Bismuth-210 has a half life of five days. If there is initially 600 milligrams, how much is left after 6 days? When will there be only 2 milligrams left? 17. The half life of carbon-14 is 5730 years.
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Unformatted text preview: how much is left after 6000 years? How long do we have to wait before there is less than 2 milligrams? 18. A certain species of bacteria doubles its population every hour. The diﬀerential equation which models this phenomenon is ˙ y = ky , where k > 0 and y is the population of bacteria at time t . What is k ? 19. If a certain microbe doubles its population every 4 hours and after 5 hours the total population has mass 500 grams, what was the initial mass?...
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