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DIFFERENTIAL EQUATIONS: Decomposition/Growth #5 only

DIFFERENTIAL EQUATIONS: Decomposition/Growth #5 only

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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DIFFERENTIAL EQUATIONS: Decomposition/Growth #5 only
Direction: solve and analyze each of the following problem in neat and orderly manner. 1. The population of a certain community follows the law of exponential change. If the present population of the community is 144,000 and ten (10) years ago wtas 100,000 when will the population double? In ten (10) years what will be thepopulation of the community? 2. The population of a country doubles in 50 years. How many years will be 5 times as much? Assume that the rate of increase is proportional to the number of habitants. 3. Radium decomposes at a rate proportional to the amount present. If half of the original amounts disappears after 1000 years, what is the percentage loss in 100 years. 4. Under a certain condition, cane sugar in water is converted into dextrose at a rate proportional to the amount that is unconverted at any time. If 75 kg at t=0, 8 kg are converted during the first 30 minutes, find the amount converted in 2 hours. 5. A certain radioactive material follows the law of exponential change and has a half-life of 38 hours. Find how long it takes for 90% of the radioactivity to be dissipated.
Transcribed Image Text:Direction: solve and analyze each of the following problem in neat and orderly manner. 1. The population of a certain community follows the law of exponential change. If the present population of the community is 144,000 and ten (10) years ago wtas 100,000 when will the population double? In ten (10) years what will be thepopulation of the community? 2. The population of a country doubles in 50 years. How many years will be 5 times as much? Assume that the rate of increase is proportional to the number of habitants. 3. Radium decomposes at a rate proportional to the amount present. If half of the original amounts disappears after 1000 years, what is the percentage loss in 100 years. 4. Under a certain condition, cane sugar in water is converted into dextrose at a rate proportional to the amount that is unconverted at any time. If 75 kg at t=0, 8 kg are converted during the first 30 minutes, find the amount converted in 2 hours. 5. A certain radioactive material follows the law of exponential change and has a half-life of 38 hours. Find how long it takes for 90% of the radioactivity to be dissipated.
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