Question

How do you determine if the equation `y=3(5/2)^x` represents exponential growth or decay?

Answer 1

Graph depicting exponential growth of `y = 3 (5/2)^x`:

graph{log y - log 3- x log ( 5/2 ) = 0 }

The ( x = 0 ) y-intercept is 3.

Note that

`y = a b^x, b > 0` is a growth function, if `b > 1` and

it decays, if `b < 1`

For the given function, `b = 5/2 > 1`.

Example for decay:

`y = 3 ( 2 / 5 )^x` decays. Here, `b = 2/5 < 1.`See graph.
graph{log y - log 3- x log ( 2/5 ) = 0 }