Explain where you see the growth factor in the graph, the table, or the equation.

To identify the growth factor in different representations like a graph, a table, or an equation, follow these insights:

1. Graph Analysis:

   • The growth factor is typically indicated by the steepness of the curve. In an exponential growth graph, the curve rises rapidly. The ratio of the function’s value at one point to its value at an earlier point will indicate the growth factor.

2. Table Examination:

   • In a table of values, the growth factor can be identified by calculating the ratio of consecutive entries. For instance, if the table reflects values of a function $f(n)$, the growth factor is determined by $\frac{f(n+1)}{f(n)}$. A consistent ratio between successive values indicates a constant growth factor.

3. Equation Recognition:

   • In equations, the growth factor can be found in models like $f(t) = f_0 \cdot r^t$ or $f(n) = ab^n$, where $r$ or $b$ represents the growth factor. If $b > 1$, it represents growth.

Conclusion

In summary, the growth factor is seen through the rate of change in the graph's slope, the ratio of values in a table, and the base of an exponential equation.