Question

How do you tell whether `f(x)=-(6/5)^-x` is an exponential growth or decay?

Answer 1

exponential decay

Explanation:

To figure out whether a function represents exponential growth or decay, we must put it in the form `f(x) = a*b^x`.

`-x` is equal to `-1 * x`, so the function becomes

`f(x) = -(6/5)^(-1*x)`

Since we know that `(a/b)^-1` is equal to `(b/a)`, we can rewrite the function in the form that we want.

`f(x) = -(5/6)^x`
or `f(x) = -1(5/6)^x`

If `0 < b < 1`, then the function represents exponential decay.
If `b > 1`, then the function represents exponential growth.

In our case, `0 < 5/6 < 1`, so this is exponential decay.