Question

1. initial value: constant ratio:

Explanation:

Step1: Find Initial Value

The initial value of a function (especially exponential) is the value when \( x = 0 \). From the table, when \( x = 0 \), \( f(x)=2 \). So initial value is 2.

Step2: Find Constant Ratio

For an exponential function, the constant ratio is found by dividing consecutive \( f(x) \) values.
Take \( \frac{f(1)}{f(0)}=\frac{6}{2} = 3 \), \( \frac{f(2)}{f(1)}=\frac{18}{6}=3 \), \( \frac{f(3)}{f(2)}=\frac{54}{18}=3 \). So constant ratio is 3.

Answer:

Initial Value: 2
Constant Ratio: 3