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

Answer:

So this is "decay".

Step-by-step explanation:

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

h = 12$(\frac{2}{3})^b$

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".

Answer 2

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.