Solve. See Example 7. The total revenue from the sale of a popular book is approximated by the rational function $R(x)=\frac{1000 x^{2}}{x^{2}+4},$ where $x$ is the number of years since publication and $R(x)$ is the total revenue in millions of dollars. a. Find the total revenue at the end of the first year. b. Find the total revenue at the end of the second year. c. Find the revenue during the second year only. d. Find the domain of function $R$.
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The total revenue from the sale of a popular book is approximated by the rational function $R(x)=\frac{1000 x^{2}}{x^{2}+4},$ where $x$ is the number of years since publication and $R(x)$ is the total revenue in millions of dollars. a. Find the total revenue at the end of the first year. b. Find the total revenue at the end of the second year. c. Find the revenue during the second year only.
Graphs and Functions
Polynomial and Rational Functions
Solve each problem. See Examples 6 and 7. A charter flight charges a fare of $\$ 200$ per person, plus $\$ 4$ per person for each unsold seat on the plane. If the plane holds 100 passengers and if $x$ represents the number of unsold seats, find the following. A. A function defined by $R(x)$ that describes the total recenue received for the flight (Hint: Multiply the number of people flying, $100-x,$ by the price per ticket, $200+4 x$.) B. The graph of the function from part (a) C. The number of unsold seats that will produce the maximum revenue D. The maximum revenue
Donna D.
If a company's revenue grows at a rate of $150 \%$ per year (rather than doubling as in Exercise 81 ), the revenue would be modeled by the function $R(t)=R_{0}\left(\frac{3}{2}\right)^{t},$ where $R_{0}$ represents the initial revenue, and $R(t)$ represents the revenue after $t$ years. (a) How much revenue is being generated after 3 yr, if the company's initial revenue was $\$ 256$ thousand? (b) How long until the business is generating $\$ 1944$ thousand in revenue? (Hint: Reduce the fraction.)
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