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2.2 Exponential Decay: Homework Exercises |
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Solve each of these |
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1. Identify each of the following as a growth or decay exponential function. Identify the growth or decay factor, the growth or decay rate, and the initial value. |
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a)
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c)
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2. Write a formula for an exponential function with initial value of 4,000 and a decay factor of |
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a) 0.75 b) 0.80 c) 0.90 |
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3. Write a formula for an exponential function with initial value of 100 and decay rate of |
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a) 2.5% b) 10% c) 33% |
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4. Suppose we were considering the population of a certain community. Suppose also that 150,000 people lived there in 2000 and that 3% of the population leave every year. How many people would be living there in 2007? |
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5. Suppose we were considering the population of a certain community. Suppose also that 500,000 people lived there in 2002 and that 7% of the population leave every year. How many people would be living there in 2008? |
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6. a) In Example 5 in the “More Worked Examples” of this section, the world oil reserve was assumed to have a rate of 3% per year. If we assume that the rate of depletion rises slightly to 5%, how much oil will be left in 50 years? |
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b) At the depletion rate of 5%, how much oil will be left in 75 years? |
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7. The population of Duel is declining exponentially. If there were 500 residents 4 years ago and half as many now, what is the yearly rate of decrease? |
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8. What was the
population 10 years ago if the current population of is 50,000? |
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