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Chapter 14: Problem 16
Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$(3 x+1)^{4}$$
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Use the formula for the sum of the first n terms of a geometric sequence to solve. You are investigating two employment opportunities. Company A offers \(\$ 30,000\) the first year. During the next four years, the salary is guaranteed to increase by \(6 \%\) per year. Company B offers \(\$ 32,000\) the first year, with guaranteed annual increases of \(3 \%\) per year after that. Which company offers the better total salary for a five-year contract? By how much? Round to the nearest dollar.
Use the formula for the sum of the first n terms of a geometric sequence to solve. A job pays a salary of \(\$ 24,000\) the first year. During the next 19 years, the salary increases by \(5 \%\) each year. What is the total lifetime salary over the 20 -year period? Round to the nearest dollar.
Use the Binomial Theorem to find a polynomial expansion for each function. Then use a graphing utility and an approach similar to the one in Exercises 69 and 70 to verify the expansion. $$f_{1}(x)=(x-1)^{3}$$
Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I modeled California's population growth with a geometric sequence, so my model is an exponential function whose domain is the set of natural numbers.
Find a general term, \(a_{n},\) for each sequence. More than one answer may be possible. $$5,7,9,11, \dots$$
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