My home uses two light bulbs. On average, a light bulb lasts for 150 days (exponentially distrvuted). When a light bulb burns out, it takes an average of 10 days (exponentially distributed) before I replace the bulb (I'm not that lazy in real world). • Formulate a three-state birth-death model of this situation. • Determine the fraction of the time that both light bulbs are working. • Determine the fraction of the time that no light bulbs are working.

My home uses two light bulbs. On average, a light bulb lasts for 150 days (exponentially distrvuted). When a light bulb burns out, it takes an average of 10 days (exponentially distributed) before I replace the bulb (I'm not that lazy in real world). • Formulate a three-state birth-death model of this situation. • Determine the fraction of the time that both light bulbs are working. • Determine the fraction of the time that no light bulbs are working.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter5: Exponential And Logarithmic Functions

Section5.2: Applications Of Exponential Functions

Problem 44E: Use a graphing calculator to solve each problem. In Example 4, suppose that a birth control program...

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IMy home uses two light bulbs. On average, a light bulb lasts for 150 days
(exponentially distrvuted). When a light bulb burns out, it takes an average of 10 days (exponentially
distributed) before I replace the bulb (I'm not that lazy in real world).
• Formulate a three-state birth-death model of this situation.
• Determine the fraction of the time that both light bulbs are working.
• Determine the fraction of the time that no light bulbs are working.

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Use a graphing calculator to solve each problem. In Example 4, suppose that a birth control program changed the formula for poulation growth to Pt=1000e0.01t. How long will the food supply be adequate? EXAMPLE 4 Using a Graphing Calculator to Solve a popuiation Problem Suppose that a country with a population of 1000 people is growing exponentially according to the population function Pt=1000e0.02t Where t in years. Furthermore, assume that the food supply, measured in adequate food per day per person, is growing linearly according to the function fx=30.625x+2000 In how many years will the population outstrip the food supply?