11-16 Class notes Exponential Growth and Decay

Linear functions have the same (constant) slope for any two points on the graph.

A function is non-linear if you can find two pairs of points on the graph with different (non-constant) slopes.

In the table on page 97, the width and length each grew by 20% or .20 with each magnification.
The growth rate is 20% or .20.

To get the new width and length for each successive magnification, you multiply the previous entries by 120% or 1.20.
The growth factor is 120% or 1.20.

The growth factor is the growth rate plus 1
g = r + 1
1.20 = .20 + 1

The growth rate is the growth factor minus 1
r = g - 1
.20 = 1.20 - 1

Negative growth rates are decay rates.
When something grows, the growth factor is greater than 1.
When something decays, the growth factor is less than 1.

In the table on page 99, the y values are halved as x increases by 1.  The growth rate is negative 50%, or -.50.  We can say that the rate of decay is 50%, or .50.

The decay factor is d = r + 1
.50 = -.50 + 1      This means each successive y is .50 or one-half the previous entry

The decay rate is r = d - 1
-.50 = .50 - 1


Homework for 11-17 is page 100, item 8