Definition: The growth factor is the number b in an exponential function y = a * b^x; each increase of 1 in x multiplies y by b.
What is the growth factor?
It is the base of the exponential. If b = 1.08, each step multiplies the quantity by 1.08, an 8% increase. If b = 0.9, each step multiplies by 0.9, a 10% decrease. Some books call b the decay factor when it is below 1.
How do you find it?
From a table with equally spaced inputs, divide each output by the previous one. From a percent rate, use b = 1 + r for increases and b = 1 – r for decreases.
Example. A table shows y = 48, 72, 108, 162 for x = 0, 1, 2, 3. Then 72 / 48 = 1.5 and 108 / 72 = 1.5, so b = 1.5 and the function is y = 48(1.5)x. This means a 50% increase per step.
What is the common error?
Reading the percent rate as the base. A 50% increase gives base 1.5, not 0.5 and not 50. Also, a factor of 1 means no change at all, and a negative base does not give a smooth exponential function.