Using Exponential and Logarithmic Functions. Scientists and researchers frequently use alternate forms of the growth and decay formulas that we used earlier.

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Presentation transcript:

Using Exponential and Logarithmic Functions

Scientists and researchers frequently use alternate forms of the growth and decay formulas that we used earlier.

* GEOLOGY The half-life of Sodium-22 is 2.6 years. Determine the value of k and the equation of decay for Sodium-22. If a is the initial amount of the substance, then the amount y that remains after 2.6 years is or 0.5a.

* HEALTH The half-life of radioactive iodine used in medical studies is 8 hours. What is the value of k for radioactive iodine?

* GEOLOGY A geologist examining a meteorite estimates that it contains only about 10% as much Sodium-22 as it would have contained when it reached the surface of the Earth. How long ago did the meteorite reach the surface of the Earth? * Let a be the initial amount of Sodium-22 in the meteorite. The amount y that remains after t years is 10% of a or 0.10a.

* HEALTH The half-life of radioactive iodine used in medical studies is 8 hours. A doctor wants to know when the amount of radioactive iodine in a patient’s body is 20% of the original amount. When will this occur?

* A. POPULATION In 2007, the population of China was 1.32 billion. In 2000, it was 1.26 billion. Determine the value of k, China’s relative rate of growth. * B. POPULATION When will China’s population reach 1.5 billion?

These functions will have a horizontal asymptote at y = c Populations cannot grow infinitely large. There are limitations, such as food supplies, living space, diseases, resources, and so on. Exponential growth is unrestricted, meaning it will increase without bound. A Logistic growth model, however, represents growth that has a limiting factor. Logistic models are most accurate models for representing population growth.

* A city’s population in millions is modeled by where t is the number of years since a. What is the horizontal asymptote? b. What is the maximum population?

A city’s population in millions is modeled by where t is the number of years since a. What will be the maximum population? b.What will be the population in 2016? c.When did the population reach 1.5 Million?