Exponential Growth and Decay

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Presentation transcript:

Exponential Growth and Decay Chapter 7 Differential Equations and Mathematical Modeling Section 7.4 Exponential Growth and Decay

Quick Review

Quick Review Solutions

What you’ll learn about The differential equation dy/dt = ky and the law of exponential change Continuously compounded interest Radioactive decay Modeling growth in convenient bases Newton’s Law of Cooling … and why Understanding the differential equation gives us new insight into exponential growth and decay.

Separable Differential Equation

Example Solving by Separation of Variables

The Law of Exponential Change

Continuously Compounded Interest

Example Compounding Interest Continuously

Example Finding Half-Life

Half-life

Newton’s Law of Cooling

Example Using Newton’s Law of Cooling A temperature probe is removed from a cup of coffee and placed in water that has a temperature of Ts = 4.5C. Temperature readings T, as recorded in the table below, are taken after 2 sec, 5 sec, and every 5 sec thereafter. Estimate the coffee’s temperature at the time the temperature probe was removed. the time when the temperature probe reading will be 8C.

Example Using Newton’s Law of Cooling