Hello,
Let's n the number of the bounce
[tex] u_{0} =100\\
u_{1} =0.7*100\\
u_{2} =0.7^{2}*100\\
u_{3} =0.7^{3}*100\\
...
u_{n} =0.7^{n} *100\\
u_{n} =0.7^{n}*100 \leq \ 1\\
[/tex]
ln(0.7^n)+ln(100) <=ln(1)
==>n*ln(0.7) <=-ln(100)
==>n >=-ln(100)/ln(0.7)
==> n>=12,911392471625765979506986280561
The ball bounces 12 times until the height is less than 1 centimetre
.
If you don't like my calculus see the file joined.
