6.4 Exponential Growth and Decay Objective: SWBAT solve problems involving exponential growth and decay in a variety of applications.

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Presentation transcript:

6.4 Exponential Growth and Decay Objective: SWBAT solve problems involving exponential growth and decay in a variety of applications

In many applications, the rate of change of a variable y is proportional to the value of y. [rate of change is a derivative] If y is a function of time t, we can express this statement as: Our goal is to solve this differential equation, meaning we have to separate the variables and get y by itself.

It will only be one or the other, the initial condition helps us figure this out (in most real situations it will be positive).

Exponential Growth and Decay The above equation represents exponential growth when k>0 and exponential decay when k<0.

Newton’s Law of Cooling Newton’s Law of Cooling states that the rate of change in the temperature of an object is proportional to the difference between the object’s temperature and the temperature in the surrounding medium. What this means is if you take a piece of pizza out of your oven, it cools off, because the temperature of your house isn’t as warm as the temperature of the oven. As a result, the pizza’s temperature will approach the temperature of your house. Hungry yet?

This problem is different from before because it is not proportional to the amount present (or the current temperature), it’s proportional to the difference between the temperature of the object at that given time, and the temperature of the medium (location of the object).

Because it isn’t directly proportional to the temperature, we have to go through the steps (we can’t just skip to the formula).