Question

A ball is dropped from a height of 10 meters. With each bounce, the height decreases by 15%(Be careful with your math here) What is the height of the ball after the 5th bounce? How many bounces must the ball take in order to be below 1 meter in height? How does this relate to a geometric sequence?

Answer 1

This is an exponential decay.

Initially, the maximum height is 10m.

After the first bounce, the height decreases by 15%, then the new maximum height is:

10m - 10m*0.15 = 10m*0.85

After the second bounce, we have another 15% decrease, the new height is:

10m*0.85 - 10m*0,85*0.15 = 10m*0.85^2

You can see now that the equation that models this situation is:

H(n) = 10m*0.85^n

Where n is the number of times that the ball bounced.

Then, if n = 5 we have that:

H(5) = 10m*0.85^5 = 4.437m

This does relate to a geometric sequence because this is an exponential (decreasing) relation.