Chapter 1: Problem 33
In Exercises \(33-36,\) solve the equation algebraically. Support your solution graphically. $$(1.045)^{t}=2$$
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Eliminating a Disease Suppose that in any given year, the number of cases of a disease is reduced by 20\(\% .\) If there are \(10,000\) cases today, how many years will it take (a) to reduce the number of cases to \(1000\)? (b) to eliminate the disease; that is, to reduce the number of cases to less than \(1\)?
In Exercises 49 and \(50,\) (a) draw the graph of the function. Then find its (b) domain and (c) range. $$f(x)=x+5, \quad g(x)=x^{2}-3$$
Enter \(y_{1}=\sqrt{x}, y_{2}=\sqrt{1-x}\) and \(y_{3}=y_{1}+y_{2}\) on your grapher. (a) Graph \(y_{3}\) in \([-3,3]\) by \([-1,3]\) (b) Compare the domain of the graph of \(y_{3}\) with the domains of the graphs of \(y_{1}\) and \(y_{2}\) . (c) Replace \(y_{3}\) by \(y_{1}-y_{2}, \quad y_{2}-y_{1}, \quad y_{1} \cdot y_{2}, \quad y_{1} / y_{2}, \quad\) and \(\quad y_{2} / y_{1}\) in turn, and repeat the comparison of part (b). (d) Based on your observations in \((b)\) and \((c),\) what would you conjecture about the domains of sums, differences, products, and quotients of functions?
Group Activity In Exercises \(33-36,\) copy and complete the table for the function. $$y=-3 x+4$$
Multiple Choice The length \(L\) of a rectangle is twice as long as its width \(W\) . Which of the following gives the area \(A\) of the rectangle as a function of its width? $$(a)A(W)=3 W \quad$$ $$(b)A(W)=\frac{1}{2} W^{2} \quad(\mathbf{C}) A(W)=2 W^{2}$$ $$(\mathbf{D}) A(W)=W^{2}+2 W \quad(\mathbf{E}) A(W)=W^{2}-2 W$$
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