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Chapter 12: Q. 66 (page 817)
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?
There are 30 rows in the corner section of a stadium.
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Initially, a pendulum swings through an arc of 2 feet. On each successive swing, the length of the arc is 0.9 of the previous length.
(a) What is the length of the arc of the 10th swing?
(b) On which swing is the length of the arc first less than 1 foot?
(c) After 15 swings, what total length will the pendulum have swung?
(d) When it stops, what total length will the pendulum have swung?
Extended Principle of Mathematical Induction The Extended Principle of Mathematical Induction states that if Conditions I and II hold, that is,
(I) A statement is true for a natural number j
(II) If the statement is true for some natural number , then it is also true for the next natural number .then the statement is true for all natural numbers . Use the Extended Principle of Mathematical Induction to show that the number of diagonals in a convex polygon of n sides is .
Trur or False:
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.
You have just signed a 7-year professional football league contract with a beginning salary of \(2,000,000 per year. Management gives you the following options with regard to your salary over the 7 years.
1. A bonus of \)100,000 each year
2. An annual increase of 4.5% per year beginning after 1 year
3. An annual increase of $95,000 per year beginning after 1 year
Which option provides the most money over the 7-year
period? Which the least? Which would you choose? Why?
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