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Chapter 14: Problem 63
Company A pays \(\$ 24,000\) yearly with raises of \(\$ 1600\) per year. Company B pays \(\$ 28,000\) yearly with raises of \(\$ 1000\) per year. Which company will pay more in year \(10 ?\) How much more?
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Solve: \(2 x^{2}=4-x\).
Use the formula for the sum of the first n terms of a geometric sequence to solve. A pendulum swings through an arc of 20 inches. On each successive swing, the length of the arc is \(90 \%\) of the previous length. $$\begin{aligned}&20, \quad\quad 0.9(20), \quad0.9^{2}(20), \quad 0.9^{3}(20), \ldots\\\&\begin{array}{|c|c|c|c|}\hline \text { 1st } & \text { 2nd } & \text { 3rd } & \text { 4th } \\\\\text { swing } & \text { swing } & \text { swing } & \text { swing } \\\\\hline\end{array}\end{aligned}$$ After 10 swings, what is the total length of the distance the pendulum has swung? Round to the nearest hundredth of an inch.
Use the formula for the value of an annuity to solve Exercises. Round answers to the nearest dollar. To save money for a sabbatical to earn a master's degree, you deposit \(\$ 2000\) at the end of each year in an annuity that pays \(7.5 \%\) compounded annually. a. How much will you have saved at the end of five years? b. Find the interest.
Use the formula for the sum of the first n terms of a geometric sequence to solve. You save \(\$ 1\) the first day of a month, \(\$ 2\) the second day, \(\$ 4\) the third day, continuing to double your savings each day. What will your total savings be for the first 15 days?
Expand and write the answer as a single logarithm with a coefficient of 1. $$\sum_{i=2}^{4} 2 i \log x$$
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