A ball is dropped from a height of 500 meters. The table below shows the height of each bounce, and the heights form a geometric sequence. How high does the ball bounce on the 8th bounce? Round your answer to the nearest meter. the common ratio is 0.80
To find the height of the ball on the 8th bounce, we can use the formula for the nth term of a geometric sequence:
an = a1 * (r^(n-1))
In this case, the first term (a1) is the height the ball is dropped from, which is 500 meters. The common ratio (r) is 0.80. We want to find the height on the 8th bounce, so n = 8.
Plugging these values into the formula, we have:
a8 = 500 * (0.80^(8-1))
= 500 * (0.80^7)
= 500 * (0.32768)
= 163.84
Therefore, the ball bounces to a height of approximately 164 meters on the 8th bounce.
To determine the height of the ball on the 8th bounce, we need to use the formula for the height of a geometric sequence, which is given by:
hn = h0 * r^(n-1)
Where:
- hn is the height of the ball on the nth bounce
- h0 is the initial height (500 meters in this case)
- r is the common ratio (0.80 in this case)
- n is the number of bounces
We can substitute the given values into the formula and solve for the height on the 8th bounce:
h8 = 500 * (0.80)^(8-1)
Simplifying the exponent:
h8 = 500 * (0.80)^7
Calculating the value of (0.80)^7:
h8 = 500 * 0.2097152
Rounding the answer to the nearest meter:
h8 ≈ 105 meters
Therefore, the ball bounces to a height of approximately 105 meters on the 8th bounce.
To find the height of the 8th bounce, we need to determine the pattern formed by the heights and then apply it.
In this case, the heights form a geometric sequence, which means each term is obtained by multiplying the previous term by a constant ratio. The common ratio is given as 0.80.
To find the height of the 8th bounce, we can use the formula:
height = initial height × (common ratio)^(n-1)
In this formula, the initial height is 500 meters, the common ratio is 0.80, and n is the number of the bounce. We want to find the height of the 8th bounce, so we substitute n = 8 into the formula:
height = 500 × (0.80)^(8-1)
Simplifying the exponent:
height = 500 × (0.80)^7
Calculating the height:
height = 500 × 0.2097152
height ≈ 104.86 meters
Rounding the answer to the nearest meter:
height ≈ 105 meters
Therefore, the ball bounces to a height of approximately 105 meters on the 8th bounce.