Question

5. For the equation below, identify and classify the

factor and rate.
y = 3624 (0.975)*
=
Student:
Decay factor is 0.975 and decay rate 0.025%
New:

Answer 1

• decay factor: 0.975
• decay rate: 2.5%

Explanation:

The decay factor is the value with the exponent.

decay factor: 0.975

The decay rate is the difference between the decay factor and 1:

0.975 -1 = -0.025 = -2.5%

decay rate: 2.5%

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Additional comment

In more general terms, we can say the value with the exponent is the "growth factor." When it is less than 1, the value of the expression decays with increasing values of the exponent. The difference between the growth factor and 1 is the "growth rate." It will be negative when the expression is describing decay (as in this problem). We often like to use positive numerical values for growth and decay rates, using their descriptor (growth rate, decay rate) to indicate the sign in the expression.

Example:

growth rate 2.5%: (1 +0.025)^t = 1.025^t

decay rate 2.5%: (1 -0.025)^t = 0.975^t