Answer:
OPTION C: The ratio is a constant.
OPTION E: The ratio is equal to b.
Step-by-step explanation:
Given: [tex]$ f(x) = a.b^x $[/tex]
The ratio of f(x + 1) and f(x) = [tex]$ \frac{f(x + 1)}{f(x)} = \frac{a.b^{x + 1}}{a.b^x} $[/tex]
Since, [tex]$ a^{x + 1} = a^x. a $[/tex]
[tex]$ \implies \frac{f(x + 1)}{f(x)} = \frac{a.b^x.b}{a.b^x} $[/tex]
Cancelling out [tex]$ a.b^x $[/tex] we get:
[tex]$ \frac{f(x + 1)}{f(x)} = b $[/tex]
This shows that the ratio is always a constant and that constant is equal to b.
