exponential notation

Question

A ball is dropped from a height of x feet. It always bounces up to 2/3 x feet. the ball is dropped from 10 feet and is caught exactly when it touches the ground after the 30th bounce. What is the total distance traveled by the ball? Express your answer in exponential notation.

Answer 1

The first bounce (the 10 foot dropped shall be considered later) is 20/3 feet.

 

The bounces form a geometric series, a₁ = 20/3, r = 2/3

 

S_n = a₁(1 - rⁿ) / (1 - r)

 

S₃₀ = 20/3(1 - (2/3)³⁰ / (1 - 2/3)

S_30 ≈ (20/3)(1 - 0.0000052150) / (1/3)

S₃₀ ≈ 20(0.999994785)

S₃₀ ≈ 19.9998957

 

Do not know why this should/could be expressed in exponential notation.