Page 723 - Algebra 1

Example
4
Application: Bounce Height
A ball is dropped from a height of 2 yards. The height of each bounce is 85% of the previous height. What is the height of the ball after 10 bounces?
SOLUTION
Understand A ball is dropped from a height of 2 yards. The height of each bounce is 85% of the height of the previous bounce. The common ratio is 85%, or 0.85.
2 yds.
? yds.
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th bounce
The heights of the bounces form a geometric sequence.
Plan Multiply the drop height of 2 yards by the common ratio 0.85 to find the height of the first bounce. This product is the 1st term of the sequence. Then use the formula A(n) = arn–1 to find the height of the 10th bounce. This is the 10th term in the sequence.
Solve Find the height of the 1st bounce: 2 · 0.85 = 1.7 yards.
So, the first term of the sequence is 1.7.
Use the formula A(n) = arn-1 to find the height of the 10th bounce.
Caution
The height of the first bounce is 1.7 yards. The first term of the sequence is 1.7, not 2. The height of the drop is 2 yards.
A( n ) = a r n - 1
A(10) = 1.7(0.85)10-1
= 1.7(0.85)9 ≈ 0.39 yards
Substitute 1.7 for a, 10 for n, and 0.85 for r. Simplify the exponent.
Simplify and round to the nearest hundredth.
Math Reasoning
Analyze Why is 1.7 multiplied by 0.85 nine times instead of ten times?
The height of the 10th bounce is about 0.39 yards.
Check Multiply the height of the first bounce by 0.85 nine times.
1.7×0.85×0.85×0.85×0.85×0.85×0.85×0.85×0.85×0.85≈0.39 ✓
Find the common ratio for each geometric sequence.
(Ex 1)
a. 2, 16, 128, 1024, ...
b. -162, 54, -18, 6, ...
c. 0.7, 4.9, 34.3, 240.1, ...
Find the next four terms of each sequence.
(Ex 2)
d. 5, -15, 45, -135, ... e. 336, 168, 84, 42, ...
Lesson Practice
708 Saxon Algebra 1