74563932_401466067166250_6548669067232804864_n.jpg - Kecana Exercises In all of the following problems assume exponen tial growth in 0.5 h However

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Unformatted text preview: Kecana Exercises In all of the following problems assume exponen- tial growth. in 0.5 h. However, bacteria are continuously 1. One estimate of the growth rate of the United siphoned off at a rate of 5 g/h. Initially, there States is 1.5% per year. How many years will it are 10 g of bacteria. How much bacteria are take for the population to double? there in the vat after 2 h? 2. A crystal grows by 5% in one day. When would 11. The rate of interest at one bank is 3% per you expect the crystal to be twice its original year, whereas the yield at another bank is 3% size? a year. Both offer continuous compounding. Find the two doubling times. 3. A certain bacterium is observed to double in 8 h. What is its growth rate? 12. The cost of a two-liter bottle of your favorite 4. The population of the world is expected to soft drink was 85 cents two years ago, but it double in the next 30 yr. What is its growth now costs 95 cents. If this rate of increase continues, approximately when will the bottle rate? cost $1.50? 5. The growth rate of a certain strain of bacteria is unknown, but assumed to be constant. When 13. The GDP (gross domestic product) of a certain an experiment started, it was estimated that country increased by 6.4% during the last year. there were about 1500 bacteria, and an hour If it continued to increase at that rate, approxi- later there were 2000. How many bacteria mately how many years would it take for the GDP to double? would you predict there are 4 h after the experiment started? 14. During one year, food prices increased by 15%. 6. A population of bacteria is initially given and At that rate, in approximately how many years grows at a constant rate k. Suppose + hours would food prices triple? later the bacteria are put into a different cul- 15. Cost of living is the amount required to pur- ture such that the population now grows at the chase a certain fixed list of goods and services constant rate k2. Determine the population of in a single year. We assume that it is subject to bacteria for all time. exponential growth. The growth rate is known 7. The doubling time for a certain virus is 3 yr. as the rate of inflation. If the cost of living rose How long will it take for the virus to increase from $10,000 to $11,000 in one year (a 10% net to 10 times its current population level? increase), what is the instantaneous rate of increase in the cost of living in that year? 8. Initially you have 0.1 g of a bacteria in a large Equivalently, what is the rate of inflation? container; 2 h later you have 0.15 g. What is the doubling time for these bacteria? 16. Over a 3-yr period, housing prices increased 15%. At that rate, how many years would it 9. An organism living in a pond reproduces at a take for housing prices to increase 50%? rate proportional to the population size. Or- ganisms also die off at a rate proportional to 17. A radioactive isotope has a half-life of 16 days. the population size. In addition, organisms are You wish to have 30 g at the end of 30 days. continuously added at a rate of k g/yr. Give How much radioisotope should you start with? the differential equation that models this 18. A radioisotope is going to be used in an exper- situation. iment. At the end of 10 days, only 5% is to be 10. A bacterium is reproducing in a large vat of left. What should the half-life be? nutrients according to an exponential growth 19. A radioactive isotope sits unused in your labo- law that would cause the population to double ratory for 10 yr, at which time it is found to...
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