Question

Select 2 of the following

Answer 1

OPTION C: The ratio is a constant.

OPTION E: The ratio is equal to b.

Explanation:

Given:
`$ f(x) = a.b^x $`

The ratio of f(x + 1) and f(x) =
`$ (f(x + 1))/(f(x)) = (a.b^(x + 1))/(a.b^x) $`

Since,
`$ a^(x + 1) = a^x. a $`

`$ \implies (f(x + 1))/(f(x)) = (a.b^x.b)/(a.b^x) $`

Cancelling out
`$ a.b^x $` we get:

`$ (f(x + 1))/(f(x)) = b $`

This shows that the ratio is always a constant and that constant is equal to b.