Respuesta :
Answer:
6th bounce: 40%
Starting amount: 100%
Decay rate: 10%
Equation: 100% - 10% - 10% - 10% - 10% - 10% - 10% =
Step-by-step explanation:
100% - 10% - 10% - 10% - 10% - 10% - 10% = 40%. 40% is the answer.
Using an exponential function, it is found that on the 6th bounce, the ball bounces up 5.31 ft.
What is an exponential function?
A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
In this problem:
- You drop a ball from a height of 10ft, hence A(0) = 10.
- Each bounce the ball gains only 90% of its height back, hence r = 0.1.
Then, the height after the nth bounce is given by:
[tex]A[n] = 10(0.9)^n[/tex]
After the 6th bounce, we have that:
[tex]A[6] = 10(0.9)^6 = 5.31[/tex]
On the 6th bounce, the ball bounces up 5.31 ft.
More can be learned about exponential functions at https://brainly.com/question/25537936
