Question

How do you determine if the equation `y = 3(0.4)^x` represents exponential growth or decay?

Answer 1

Exponential Decay

Explanation:

Take a look at the equation: `y = a * b^x`

When `b > 1`, the equation represents exponential growth. When `b` is between `0` and `1`, the equation represents exponential decay.

The equation `y=3(0.4)^x` represents exponential decay, since `b`, or `0.4`, is greater than `0` and less than `1`.

Look at the graph to confirm exponential decay.
graph{3(0.4)^x [-6.71, 13.29, -2.17, 8.25]}

Answer 2

The eqn. represents decay.

Explanation:

We know that, the function `a^x` is `uarr` for `a>1` and it is `darr` for `0<,a<,1`

`:. (0.4)^x` is `darr` & so is `y=3(0.4)^x`

Therefore, the eqn. represents decay.