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Chapter 14: Problem 24
Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$(c+3)^{5}$$
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Use the formula for the general term (the nth term) of a geometric sequence to solve. A professional baseball player signs a contract with a beginning salary of \(\$ 3,000,000\) for the first year and an annual increase of \(4 \%\) per year beginning in the second year. That is, beginning in year \(2,\) the athlete's salary will be 1.04 times what it was in the previous year. What is the athlete's salary for year 7 of the contract? Round to the nearest dollar.
Explain how to find the sum of the first \(n\) terms of a geometric sequence without having to add up all the terms.
Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. It makes a difference whether or not I use parentheses around the expression following the summation symbol, because the value of \(\sum_{i=1}^{6}(i+7)\) is \(92,\) but the value of \(\sum_{i=1}^{8} i+7\) is 43.
For the first 30 days of a flu outbreak, the number of students on your campus who become ill is increasing. Which is worse: the number of students with the flu is increasing arithmetically or is increasing geometrically? Explain your answer.
Factor: \(27 x^{3}-8\) (Section 6.4, Example 8)
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