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Modeling Exponential Growth and Decay in Real-Life Situations

This section covers the application of exponential equations using logarithms to model real-life scenarios. We explore various situations including home appreciation, car depreciation, population growth of alligators, radioactive decay of Sr-85, and investment growth. Each example provides a practical approach to understanding how to calculate timeframes for accruing value or decline based on percentage rates. Students will learn to formulate exponential models and solve questions related to these scenarios, utilizing logarithmic functions for detailed analysis.

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Modeling Exponential Growth and Decay in Real-Life Situations

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  1. Exponential Equations Using Logarithms Section 8-5

  2. Write an exponential model for each situation. Then, answer the question. • The price of a new home is $210,000. The value of the home appreciates 2% each year. How long will it take the home to be worth $300,000? • A new car that sells for $25,000 depreciates 22% each year. How long will it take for the car to be worth $15,000?

  3. In Lake Derf, there are currently 32 alligators. The gator population is increasing at an annual rate of 17%. How long will it take for the lake to have 50 gators?

  4. Sr-85 is used in bone scans. It has a half-life of 64.9 days. Write the exponential function for an 8-mg sample. How long will it take for there to be 5 mg left?

  5. 5. Suppose you invest $5000 at an annual interest rate of 3%. How long will it take your investment to double if it is compounded quarterly?

  6. Solutions to page 456 • 0.05 • 0.3162 • 33 • 10,000 • 1/60 • 12 • 315.2 • 2 • 1.5850 • 2.1240 • 2.7320 • 3.0101 • 3 • 3.4650 • 0.9534 • 0.3579 • 3.2056 • 0.2720 • 300,000,000 • 223,606.8 • 5 • ¼ • 1357.2 • 7 • 79. 2.9315 • 81. 0.6225 • 2.3094 • 85. 0.8505 • 87. 7.4168 • 89. 2.9615 • 91. 1 • 93. 1.0451 • 95. 1.3063

  7. Homework Page 456 #31, 32, 50-52, 80-104 even, 99

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