Exponential Decay

Exponential Decay

Example 1

For her fifth birthday, Nadia's grandmother gave her a full bag of candy. Nadia counted her candy and found out that there were 160 pieces in the bag. As you might suspect Nadia loves candy so she ate half the candy on the first day. Her mother told her that if she eats it at that rate it will be all gone the next day and she will not have any more until her next birthday.

Nadia devised a clever plan. She will always eat half of the candy that is left in the bag each day. She thinks that she will get candy every day and her candy will never run out. How much candy does Nadia have at the end of the week? Would the candy really last forever?

Step 1. Determine the initial value.

Since the first day she had 160 pieces of candy, the initial value is 160.

Step 2. Determine the decay factor.

Since she is eating half the candy every day, it is being multiplied by 0.5 each day. Therefore, the decay factor is 0.5.

Step 3. Write an exponential function.

The general form of an exponential function is ExpDecayEx1-1.

For this situation, the equation is ExpDecayEx1-2.