- Estimate In Exercises 15 22 Assume That B Is A Positive Number And That U And V Are Fixed Numbers So That B 3 And B 1 (47.41 KiB) Viewed 28 times
- Estimate In Exercises 15 22 Assume That B Is A Positive Number And That U And V Are Fixed Numbers So That B 3 And B 2 (73.76 KiB) Viewed 28 times
25. Suppose you invest a certain amount of money at 6% in- 32. Suppose a certain quantity of radon gas decayed to 400 terest, compounded annually. By what factor will your investment increase after 7 years? after 12 years? cubic centimeters over a period of 8 days. How much was there to begin with? (Hint: Refer to Eq. (7).) 26. How much money should be put in an account paying 5% interest, compounded annually, in order to have $5,000 eight years from now? (Hint: Write the formula for the amount after eight years on an initial investment of P dol- lars, set it equal to 5,000, and solve for P.) 27. How much money should be put in an account paying 4% interest, compounded annually, in order to have $50,000 twenty years from now? 28. Which of the following will yield the greater amount: (a) putting $1,000 in an account paying 3% interest, com- pounded annually, and leaving it for 10 years, or (b) putting $1,000 in an account paying 6% interest, compounded an- nually, and leaving it for 5 years? 29. A certain bacteria culture grows exponentially. In 1 hour the population grows from 500,000 to 800,000. Write a formula expressing the population P as a function of the time in hours. 30. A colony of fruit flies is growing exponentially. At the beginning there were 3,000 flies, and the end of 3 days there were 7,000 flies. (a) Write a formula expressing the population P as a func- tion of the time t in days. (b) Determine how many flies there will be at the end of 5 days. 127 33. A certain radioactive substance decays in accordance with the formula y = y(0.88)', where yo is the initial amount and y is the amount after r years. What percentage of the original amount will be left after 5 years? 34. A certain radioactive substance decays in accordance with the formula y = yo(0.93), where yo is the initial amount and r is the time in days. If there are 200 grams of the substance at the end of the third day, how many will there be at the end of the fifth day? 35. Plutonium-230 is a radioactive substance, whose decay equation has the form y yob', where y is the amount at the end of r years. An initial amount of 50 milligrams of plutonium-230 decays to approximately 30 milligrams in t 10 years. (a) Use the given data to find the constants yo and b. Round your answer to two decimal places. (You can use a calculator for b, but you shouldn't need one to find yo-) (b) How much of the initial 50 milligrams will be left at the end of 20 years? (c) Suppose the initial amount is 80 milligrams. How much will be left at the end of 15 years? 36. Suppose $1,000 is invested at an annual interest rate of 4.5%. Create a table of values and a chart of A(r), the amount after years, fort from 1 to 25.