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Applications of Exponential Functions

Applications of Exponential Functions. Radioactive Decay. The amount A of radioactive material present at time t is given by Where A 0 is the initial amount at t=0 and h is the material’s half-life. Example 1:.

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Applications of Exponential Functions

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  1. Applications of Exponential Functions

  2. Radioactive Decay The amount A of radioactive material present at time t is given by Where A0 is the initial amount at t=0 and h is the material’s half-life.

  3. Example 1: The half-life of radium is approximately 1600 years. How much of a 1-gram sample will remain after 1000 years?

  4. Example 1Solution: 0.65 g remainsafter 1000 yrs.

  5. Oceanography The intensity I of light (in lumens) at a distance x meters below the surface of a body of water decreases exponentially by: where I0 is the intensity of light above the water.

  6. Example 2: For a certain area of the Atlantic Ocean, I0=12 and k=0.6. Find the intensity of light at a depth of 5 meters in this body of water.

  7. Example 2: Given I0=12 and k=0.6 and x=5 : lumens

  8. Malthusian Population Growth • Malthusian model for Population Growth assumes a constant birth rate (b) and death rate (d). It is as follows: where k=b - d , t is time in years, P is current population, and P0 the initial population.

  9. Example 3: The population of the U.S. is approximately 300 million people. Assuming the annual birth rate is 19 per 1000 and the annual death rate is 7 per 1000. What does the Malthusian model predict the population will be in 50 years?

  10. Example 3: Given: b=0.019 , d=0.007, P0 =300 million, t=50 Prediction in 50 years

  11. Epidemiology

  12. Example 4: • In a city with a population of 1,200,000, there are currently 1,000 cases of infection with HIV. • Using the formula: • How many people will be infected in 3 years?

  13. Example 4: Infected in 3 years

  14. Example 5:

  15. Example 5: Using our graphing calculator, the approximate intersection of the two functions at (71,4160) gives usthe prediction:In about 71 yrs the food supply will be outstrippedby population of about 4160.

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