Question

in his physics class, Mario discovered the height, h, in feet of a bouncing basketball after b bounces is given by the formula: h=12(2/3)b is this growth or decay

Answer 1

This is a geometric sequence which represent exponential decay. For any sequence, if r^2, the common ratio squared, is less than one, it is exponential decay, or:

f=ir^t

If r^2<1, it is exponential decay. In this case r=2/3, so it is exponential decay.

Answer 2

So this is "decay".

Explanation:

In a physics class Mario discovered the height h of bouncing basketball after b bounces is given by the formula

h = 12
`((2)/(3))^b`

Since for a geometric sequence explicit formula is given by

`T_(n)=a(r)^(n-1)`

Where r is in the fraction then the sequence will be convergent or decreasing.

So this is "decay".