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2.4 Continuous Growth and Decay: Homework Exercises |
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Solve each of these |
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1. Write a formula for continuous decay at 1.25% annually with initial value of |
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a) 2,500 |
b) 3,000 |
c) 2 |
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2. How much money would be in an account after 20 years if you deposited $15,000 at each of the following interest annually rates compounded continuously? |
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a) 1.2% |
b) 28% |
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c) 6.56% |
d) 4.75% |
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3. Which is the better deal: An account that pays 8% interest compounded daily or one that pays 7.95% compounded continuously? |
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4. Which is the better deal: An account that pays 4% interest compounded daily or one that pays 3.95% compounded continuously? |
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5. Find how much money you would need to invest in an account that gives 7.3% interest compounded continuously if you want to have $50,000 in this account in 15 years. |
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6. Find how much money you would need to invest in an account that gives 6.5% interest compounded continuously if you want to have $100,000 when you retire in 40 years. |
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7. Find how much money you would need to invest in an account that gives 3% interest compounded continuously if you want to have $2500 for a car down payment in 3 years? |
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8. The number of people in a small population after t years is given by |
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a) Is the population growing or shrinking? |
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b) What is the initial number in the population? |
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c) How large is the population after 10 years? |
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9. The number of people in a larger population after t years is given by |
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a) Is the population growing or shrinking? |
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b) What is the initial number in the population? |
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c) How large is the population after 10 years? |
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10. Given that an amount (in grams) of radioactive material decays in such a way |
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that after t years, the amount left is given by |
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a) What is the initial amount of radioactive material? |
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b) How much radioactive material remains after 700 years? |
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