A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce: f(n) = 9(0.7)n What does the number 9 in the function represent?

Accepted Solution

Answer:9 represents the initial height from which the ball was droppedStep-by-step explanation:Bouncing of a ball can be expressed by a Geometric Progression. The function for the given scenario is:[tex]f(n)=9(0.7)^{n}[/tex]The general formula for the geometric progression modelling this scenario is:[tex]f(n)=f_{0}(r)^{n}[/tex]Here,[tex]f_{0}[/tex] represents the initial height i.e. the height from which the object was dropped.r represents the percentage the object covers with respect to the previous bounce.Comparing the given scenario with general equation, we can write:[tex]f_{0}[/tex] = 9r = 0.7 = 70%i.e. the ball was dropped from the height of 9 feet initially and it bounces back to 70% of its previous height every time.