The height f(x)80(0.5)x. How many times higher is the first bouncee than the fourth bounce?

To find out how many times higher the first bounce is than the fourth bounce using the function ( f(x) = 80(0.5)^x ), we calculate ( f(1) ) and ( f(4) ).

First bounce: ( f(1) = 80(0.5)^1 = 40 ).
Fourth bounce: ( f(4) = 80(0.5)^4 = 80(0.0625) = 5 ).

Now, to find how many times higher the first bounce is than the fourth, we divide ( f(1) ) by ( f(4) ):
[ \frac{f(1)}{f(4)} = \frac{40}{5} = 8. ]

Thus, the first bounce is 8 times higher than the fourth bounce.