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Chapter 3: Problem 5
Approximate each number using a calculator. Round your answer to three decimal places. $$4^{-1.5}$$
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The exponential growth models describe the population of the indicated country, \(A\), in millions, \(t\) years after 2006 $$\begin{array{l}\mathrm{Camada}\quadA=33.1e^{0.009\mathrm{t}}\\\\\mathrm{U}_{\mathrm{ganda}}\quad A=28.2 e^{0.034 t}\end{array}$$ In Exercises \(81-84,\) use this information to determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The models indicate that in \(2013,\) Uganda's population will exceed Canada's.
The formula \(S=C(1+r)^{t}\) models inflation, where \(C=\) the value today, \(r=\)the annual inflation rate, and \(S=\)the inflated value t years from now. Use this formula to solve. Round answers to the nearest dollar. If the inflation rate is \(6 \%,\) how much will a house now worth \(\$ 465,000\) be worth in 10 years?
In Exercises \(125-132,\) use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution set. Verify this value by direct substitution into the equation.. $$3^{x}=2 x+3$$
Hurricanes are one of nature's most destructive forces. These low-pressure areas often have diameters of over 500 miles. The function \(f(x)=0.48 \ln (x+1)+27\) models the barometric air pressure, \(f(x),\) in inches of mercury, at a distance of \(x\) miles from the eye of a hurricane. Use this function to solve Exercises \(133-134\) Graph the function in a [0,500,50] by [27,30,1] viewing rectangle. What does the shape of the graph indicate about barometric air pressure as the distance from the eye increases?
Graph \(f\) and \(g\) in the same rectangular coordinate system. Then find the point of intersection of the two graphs. Graph \(y=2^{x}\) and \(x=2^{y}\) in the same rectangular coordinate system.
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