This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1922 Excerpt: ...Q which decreases in an analogous manner. EXERCISES 1. Find the amount of $1500 after t years with interest at 5%, compounded continuously. How much after ten years? 2. At what rate, compounding annually, would the final amount be the same as in Ex. 1? 3. In Ex. 1, when would the amount be $5000? 4. An investment ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1922 Excerpt: ...Q which decreases in an analogous manner. EXERCISES 1. Find the amount of $1500 after t years with interest at 5%, compounded continuously. How much after ten years? 2. At what rate, compounding annually, would the final amount be the same as in Ex. 1? 3. In Ex. 1, when would the amount be $5000? 4. An investment depreciated at a constant percentage rate of 6%, starting from an original value of $75,000. What was its value after t years? After 10 yr.? ' 5. In Ex. 4, what percentage was actually lost per year? '" J 6. In 1870 the population of a certain city (Portland, Ore.) was 8300, and this grew until 1910 almost like an investment with interest at 8%, compounded continuously. (a) Write a formula for the population at any time (t years after 1870), on this basis. (6) Compare the population in 1900 and in 1910 (90,500 and 207,200) with the values given by your formula. If the formula had remained valid, what would the 1920 population have been? 7. The number of bacteria in a culture increased at a rate (per hour) always equal to 30% of the number. Find how many there were at any time from an original 100. How many after 5 hours? 8. In Ex. 7, when had the original number doubled? _, 9. Radium decomposes at a rate (per century) which at every instant equals 3.8% of the quantity Q remaining. How much will be left after 1000 years from a present quantity of 100 mg.? 10. The speed (V) of a rotating wheel after the power was cut off decreased at a rate (per sec.) which at every instant was 25% of V itself. If V was originally 1000, what was its value after 10 sec? When was the speed reduced to one tenth its original value? 11. The speed (V) of a chemical reaction increases with the temperature (T) at a rate constantly equal to 7% of V. If V=30 when T = 0, w...
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