Lesson #5 Exponential Relations May 17, 2011

When Exponential Relations are graphed, they are curved lines When Exponential Relations are graphed, they are curved lines. However, unlike linear and quadratic relations, exponential relations represent a change based on ratios instead of differences. We can find trends in the equations, graphs, and table of values with exponential relations as we did with linear and quadratic relations.

1. Equations The form y = abx is how all relations that are exponential can be expressed. (where a represents the ___initial value______ and b represents the ___growth or decay rate___) The key thing to remember is that x is the exponent. Recall from unit 3: if the base (b) is between 0 and 1 (it is a decimal), the relation models exponential decay. if the base is greater than 1, the relation models exponential growth.

Examples of exponential equations: y = 3(2)x b) P = 100 (2)t c)y = 2(0.25)x

2. Graphs When graphed, exponential relations are curved lines that increase or decrease more and more rapidly, or more and more slowly. Exponential relations do not have symmetry and they do not have a maximum or minimum point. They are, in theory, continuous and infinite.

3. Table of Values Exponential Relations change at a constant percent rate. They have growth or decay factors that are equal. To prove this using a table of values, use the dependent values (y-values) only. Dividing a y- value by the previous y-value will produce a CONSTANT RATIO.

Therefore, the growth factor is ___1.4____. Example1: Consider this table. Decide if it is exponential by comparing the ratios x y 3.5 1 4.9 2 6.9 3 9.6 4 13.4 5 18.8 Therefore, the growth factor is ___1.4____.

Which are exponential models Which are exponential models? Find the exponential growth/decay factor if the table is exponential. x y 7 2 63.1 1 15.4 4 5 37.1 33.9 6 10 21.8 3 74.6 8 15 12.8 164.1 9 20 7.5 361.1 25 4.4 794.3 12 30 2.6 1747.5 14 35 1.5 Table 1:Growth is 2.2 Table 2: Linear, not exponential Table 3: Decay is 0.59