Exponential Growth and Decay Foldable Notes for Algebra 1 - Free Printable

Final Answer:
The exponential growth equation is $ y = a \cdot b^x $ with $ b > 1 $, and the exponential decay equation is $ y = a \cdot b^x $ with $ 0 < b < 1 $. For the given tables:
- Growth table fits $ y = 2 \cdot 1.5^x $ (since values double then triple roughly, and ratio between successive terms is 1.5).
- Decay table fits $ y = 9 \cdot \left(\frac{1}{3}\right)^x $ (since each term is one-third of the previous: 9 → 3 → 1 → 1/3 → ...).

But since the question likely asks for the *general form* matching each case (as shown in the diagram), the final answers are:

For growth: $ y = a \cdot b^x $, where $ b > 1 $
For decay: $ y = a \cdot b^x $, where $ 0 < b < 1 $

However, if a single boxed answer is required per standard format, and based on the labeled “equation” sections in the image (which show examples like $ y = 2 \cdot 1.5^x $ and $ y = 9 \cdot (1/3)^x $), the specific equations fitting the tables are:

Growth: $ y = 2 \cdot \left(\frac{3}{2}\right)^x $
Decay: $ y = 9 \cdot \left(\frac{1}{3}\right)^x $

Since the task appears to ask to identify or write the correct equations for the two tables, and the tables are:

Growth table:
x: −2, −1, 0, 1, 2
y: 8/9, 4/3, 2, 3, 9/2

Check ratios:
$ \frac{4/3}{8/9} = \frac{4}{3} \cdot \frac{9}{8} = \frac{36}{24} = 1.5 $
$ \frac{2}{4/3} = 2 \cdot \frac{3}{4} = 1.5 $
$ \frac{3}{2} = 1.5 $, etc. So common ratio $ b = 1.5 = \frac{3}{2} $
When $ x = 0 $, $ y = 2 $, so $ a = 2 $.
→ Equation: $ y = 2 \cdot \left(\frac{3}{2}\right)^x $

Decay table:
x: −2, −1, 0, 1, 2
y: 81, 27, 9, 3, 1

Ratios:
$ \frac{27}{81} = \frac{1}{3} $, $ \frac{9}{27} = \frac{1}{3} $, etc. So $ b = \frac{1}{3} $
When $ x = 0 $, $ y = 9 $, so $ a = 9 $.
→ Equation: $ y = 9 \cdot \left(\frac{1}{3}\right)^x $

Thus, the two correct equations are:

$ y = 2 \cdot \left(\frac{3}{2}\right)^x $ and $ y = 9 \cdot \left(\frac{1}{3}\right)^x $

But the instruction says: *Provide only the final correct answer.* Since there are two parts, and typical format expects both, we present them clearly:

Final Answer:
$ y = 2 \cdot \left(\frac{3}{2}\right)^x $ and $ y = 9 \cdot \left(\frac{1}{3}\right)^x $