A rubber ball bounces after it is dropped from a height of 212 feet, and it continues to bounce one-half the height from which it last fell. How many
bounces does it take
before the ball falls less than one foot?

C. 8 bounces

Step-by-step explanation:

To solve this, you can write an equation before turning it into an inequality:

y = 212*(1/2^x)

(x is bounces, y is height)

Now you can change it into an inequality to fit the height of less than 1:

1 > 212*(1/2^x)

In order for the right side of the equation to be less than 1, 2^x must be greater than 212 (because 212*(1/212) is 1, so if the denominator is greater, it'll be less than 1). 2^8 is 256, which is greater than 212, so that means x is 8.

Because x represents bounces, that means the ball's height will be under 1 foot after 8 bounces.

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step-by-step explanation: