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Chapter 12: Q 5. (page 824)
True or False: In a geometric sequence the common ratio is always a positive number.
The statement : In a geometric sequence the common ratio is always a positive number is false.
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A ball is dropped from a height of 30 feet. Each time it strikes the ground, it bounces up to 0.8 of the previous height.
(a) What height will the ball bounce up to after it strikes the ground for the third time?
(b) How high will it bounce after it strikes the ground for the nth time?
(c) How many times does the ball need to strike the ground before its bounce is less than 6 inches?
(d) What total distance does the ball travel before it stops bouncing?
Jodi and Jeff borrowed \(120,000 at 6.5% per annum compounded monthly for 30 years to purchase a home. Their monthly payment is determined to be \)758.48.
(a) Find a recursive formula for their balance after each monthly payment has been made.
(b) Determine Jodi and Jeff鈥檚 balance after the first payment.
(c) Using a graphing utility, create a table showing Jodi and Jeff鈥檚 balance after each monthly payment.
(d) Using a graphing utility, determine when Jodi and Jeff鈥檚 balance will be below \(100,000.
(e) Using a graphing utility, determine when Jodi and Jeff will pay off the balance.
(f) Determine Jodi and Jeff鈥檚 interest expense when the loan is paid
(h) Is it worthwhile for Jodi and Jeff to pay the additional \)100? Explain.
A ball is dropped from a height of 20 feet. Each time it strikes the ground, it bounces up to three-quarters of the previous height.
(a) What height will the ball bounce up to after it strikes the ground for the third time?
(b) How high will it bounce after it strikes the ground for the nth time?
(c) How many times does the ball need to strike the ground before its bounce is less than 6 inches?
(d) What total distance does the ball travel before it stops bouncing?
Stadium Construction: How many rows are in the corner section of a stadium containing 2040 seats if the first row has 10 seats and each successive row has 4 additional seats?
Use the Binomial Theorem to find the numerical value of
(0.998)6 correct to five decimal places.
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