A ball is dropped from a height of 30 feet and each time it hits the ground it bounces 0.75 of the previous height. What is the height of the ball after it makes its third bounce? Round to the nearest hundredth of a foot

12.66 ft.

Step-by-step explanation:

30*.75 = 22.5

22.5*.75 = 16. 875

16.875*.75 = 12.65625

12.656 rounded to the nearest hundredth is 12.66

or...

since you write it as 30*.75*.75*.75, a faster way is

30*.75^3 = 12.66

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: